Updated on 2022/12/27

写真a

 
TAKAHASHI Norikazu
 
Organization
Faculty of Natural Science and Technology Professor
Position
Professor
External link

Degree

  • Doctor of Engineering ( Kyushu University )

Research Interests

  • 非線形システム

  • 情報数理工学

  • Nonlinear Systems

  • Optimization

  • Graph Theory

  • Network Science

  • Information and Mathematical Engineering

  • 最適化

  • グラフ理論

  • ネットワーク科学

Research Areas

  • Informatics / Theory of informatics

Education

  • Kyushu University   工学研究科   情報工学専攻

    - 1996

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    Country: Japan

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  • Kyushu University    

    - 1996

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  • Kyushu University   工学研究科   情報工学専攻

    - 1993

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    Country: Japan

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  • Kyushu University    

    - 1993

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  • Kyushu University    

    - 1991

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  • Kyushu University   工学部   情報工学科

    - 1991

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    Country: Japan

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Research History

  • Visiting Professor,Kumamoto University

    2014 - 2015

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  • Kumamoto University

    2014 - 2015

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  • - Professor,Graduate School of Natural Science and Technology,Okayama University

    2013

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  • - 岡山大学自然科学研究科 教授

    2013

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  • Institute of Systems, Information Technologies and Nanotechnologies

    2008 - 2016

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  • Associate Professor

    2007 - 2013

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  • Kyushu University

    2007 - 2013

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  • Associate Professor

    1998 - 2007

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  • Kyushu University

    1998 - 2007

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  • Research Associate

    1996 - 1998

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  • Kyushu University

    1996 - 1998

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  • Visiting Scholar,University of California, Berkeley

    1996 - 1997

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  • University of California, Berkeley

    1996 - 1997

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Professional Memberships

Committee Memberships

  • おかやまAI・セキュアIoT共創コンソーシアム   会長  

    2020.3   

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    Committee type:Other

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  • 電子情報通信学会非線形問題研究専門委員会   委員長  

    2018.6 - 2019.5   

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    Committee type:Academic society

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  • 電子情報通信学会非線形問題研究専門委員会   副委員長  

    2017.6 - 2018.5   

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    Committee type:Academic society

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Papers

  • A faster algorithm to search for generalized Moore graphs Reviewed

    Taku Hirayama, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2022 IEEE Region 10 Conference   1 - 6   2022.11

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    DOI: 10.1109/tencon55691.2022.9977538

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  • Deep learning of OpenStreetMap images labeled using road traffic accident data Reviewed

    Kaito Arase, Zhijian Wu, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2022 IEEE Region 10 Conference   1 - 6   2022.11

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    DOI: 10.1109/tencon55691.2022.9977529

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  • A novel update rule of HALS algorithm for nonnegative matrix factorization and Zangwill’s global convergence Reviewed

    Takehiro Sano, Tsuyoshi Migita, Norikazu Takahashi

    Journal of Global Optimization   84   755 - 781   2022.11

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    Nonnegative Matrix Factorization (NMF) has attracted a great deal of attention as an effective technique for dimensionality reduction of large-scale nonnegative data. Given a nonnegative matrix, NMF aims to obtain two low-rank nonnegative factor matrices by solving a constrained optimization problem. The Hierarchical Alternating Least Squares (HALS) algorithm is a well-known and widely-used iterative method for solving such optimization problems. However, the original update rule used in the HALS algorithm is not well defined. In this paper, we propose a novel well-defined update rule of the HALS algorithm, and prove its global convergence in the sense of Zangwill. Unlike conventional globally-convergent update rules, the proposed one allows variables to take the value of zero and hence can obtain sparse factor matrices. We also present two stopping conditions that guarantee the finite termination of the HALS algorithm. The practical usefulness of the proposed update rule is shown through experiments using real-world datasets.

    DOI: 10.1007/s10898-022-01167-7

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  • An algorithm for updating betweenness centrality scores of all vertices in a graph upon deletion of a single edge Reviewed

    Yoshiki Satotani, Tsuyoshi Migita, Norikazu Takahashi

    Journal of Complex Networks   10 ( 4 )   2022.8

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Oxford University Press (OUP)  

    Abstract

    Betweenness centrality (BC) is a measure of the importance of a vertex in a graph, which is defined using the number of the shortest paths passing through the vertex. Brandes proposed an efficient algorithm for computing the BC scores of all vertices in a graph, which accumulates pair dependencies while traversing single-source shortest paths. Although this algorithm works well on static graphs, its direct application to dynamic graphs takes a huge amount of computation time because the BC scores must be computed from scratch every time the structure of graph changes. Therefore, various algorithms for updating the BC scores of all vertices have been developed so far. In this article, we propose a novel algorithm for updating the BC scores of all vertices in a graph upon deletion of a single edge. We also show the validity and efficiency of the proposed algorithm through theoretical analysis and experiments using various graphs obtained from synthetic and real networks.

    DOI: 10.1093/comnet/cnac033

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  • Uncalibrated photometric stereo using superquadrics with texture estimation Reviewed

    Tsuyoshi Migita, Ayane Okada, Norikazu Takahashi

    Proceedings of the 28th International Workshop on Frontiers of Computer Vision (Communications in Computer and Information Science, vol.1578)   34 - 48   2022.5

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    When a 3D scene is captured in several 2D images, a compact description (or parameters) of the 3D scene can be estimated from the images. Such an inference is formulated as the inverse of rendering computer graphics and is important for various applications, such as object recognition, inspection, and/or VR. In the present paper, we extend a photometric stereo method in such a way as to estimate the texture of the object in addition to previous estimation of parameters describing the objects and light sources. To do so, we need a realistic minimization method, combined with a method to obtain the Jacobian of the cost function with respect to the texture. We implemented this method and verified the validity of the framework using synthetic and real-world data.

    DOI: 10.1007/978-3-031-06381-7_3

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  • Distributed HALS algorithm for NMF based on simple average consensus algorithm Reviewed

    Keiju Hayashi, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2021 IEEE International Conference on Progress in Informatics and Computing   41 - 47   2021.12

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  • An algorithm for randomized nonnegative matrix factorization and its global convergence Reviewed

    Takao Masuda, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2021 IEEE Symposium Series on Computational Intelligence   1 - 7   2021.12

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  • Uncalibrated photometric stereo using superquadrics with cast shadow Reviewed

    Takumi Nasu, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 27th International Workshop on Frontiers of Computer Vision (Communications in Computer and Information Science, vol.1405)   267 - 280   2021.7

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer International Publishing  

    DOI: 10.1007/978-3-030-81638-4_22

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  • A genetic algorithm for finding regular graphs with minimum average shortest path length Reviewed

    Reiji Hayashi, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2020 IEEE Symposium Series of Computational Intelligence   2431 - 2436   2020.12

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    Authorship:Last author, Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    The problem of finding a simple regular graph with the specified order and degree that minimizes the average shortest path length has a long history in graph theory. Recently this problem has attracted a great deal of attention in relation to the design of computer networks in data centers. In this paper, we propose a genetic algorithm for finding an approximate solution to this problem. Because the search space is the set of all simple regular graphs with the specified order and degree, conventional genetic algorithms cannot be directly applied. We propose in this paper new crossover and mutation operators that guarantee the simplicity and regularity of graphs. We also evaluate the effectiveness of the proposed method experimentally.

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  • Distributed algorithm for principal component analysis based on power method and average consensus algorithm Reviewed

    Norikazu Takahashi, Mutsuki Oura, Tsuyoshi Migita

    Proceedings of the 2020 International Conference on Progress in Informatics and Computing   120 ( 26(NLP2020 1-10) )   16 - 21   2020.12

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  • Element-wise alternating least squares algorithm for nonnegative matrix factorization on one-hot encoded data Reviewed

    Zhuo Wu, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 27th International Conference on Neural Information Processing (Communications in Computer and Information Science, vol.1333)   71st   342 - 350   2020.11

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    Authorship:Last author, Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer International Publishing  

    DOI: 10.1007/978-3-030-63823-8_40

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  • Uncalibrated photometric stereo using quadric surfaces with two cameras Reviewed

    Takumi Nasu, Tsuyoshi Migita, Takeshi Shakunaga, Norikazu Takahashi

    Proceedings of the 26th International Workshop on Frontiers of Computer Vision (Communications in Computer and Information Science, vol.1212)   1212   318 - 332   2020

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    Language:English   Publishing type:Part of collection (book)   Publisher:Springer Singapore  

    Inverse rendering is a method for estimating object shapes and lighting conditions from a set of images. In the present paper, we propose an uncalibrated photometric stereo method that approximates the shapes of the target objects using quadric surfaces (ellipsoids or hyperboloids), and this shape representation allows us to use multiple cameras in order to reduce the GBR ambiguity. The proposed method uses the Levenberg-Marquardt method to minimize the differences between the input images and generated images calculated based on the estimated parameters and the image formation model. It is important to define each term in the cost function depending on the inside or outside of the contour of the estimated quadric surface and/or the target object. The proposed method has been verified on several sets of real images, namely, Vase, Grapes, and Snacks, and we found that the method required less than 100 iterations. On the other hand, there is room for improvement regarding the accuracy of the estimation by taking into account the shadows of the target objects and using a more advanced reflection model.

    DOI: 10.1007/978-981-15-4818-5_24

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  • New rules for choosing values of consensus weights in distributed training of neural networks Reviewed

    Kazuaki Harada, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2019 International Symposium on Nonlinear Theory and Its Applications   17 - 20   2019.12

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  • A distributed HALS algorithm for Euclidean distance-based nonnegative matrix factorization Reviewed

    Yohei Domen, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2019 IEEE Symposium Series on Computational Intelligence   1333 - 1338   2019.12

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    Authorship:Last author, Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    This paper proposes a distributed algorithm for multiple agents to perform the Nonnegative Matrix Factorization (NMF) based on the Euclidean distance. The matrix to be factorized is partitioned into multiple blocks, and each block is assigned to one of the agents forming a two-dimensional grid network. Each agent handles a small number of entries of the factor matrices corresponding to the assigned block, and updates their values by using information coming from the neighbors. It is shown that the proposed algorithm simulates the hierarchical alternating least squares method, which is well known as a fast algorithm for NMF based on the Euclidean distance, by making use of a finite-time distributed consensus algorithm.

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  • An infinity norm-based pseudo-decentralized discrete-time algorithm for computing algebraic connectivity Reviewed

    Katsuki Shimada, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2019 IEEE Symposium Series on Computational Intelligence   1292 - 1298   2019.12

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    In some applications of multiagent networks, it is desired that each agent can evaluate how well the network is connected. In this paper, we propose a novel discrete-time algorithm for each agent to compute the algebraic connectivity of the network in a pseudo-decentralized manner. The proposed algorithm requires less computational cost than the conventional algorithm. We also analyze the dynamical behavior of the proposed algorithm and prove under some assumptions on the parameter values and the initial state values of the agents that all agents can compute the algebraic connectivity.

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  • A genetic algorithm for maximizing algebraic connectivity of graphs by adding multiple edges Reviewed

    Hiroki Tajiri, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2019 International Symposium on Nonlinear Theory and Its Applications   138 - 141   2019.12

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  • Mutual relationship between the neural network model and linear complexity for pseudorandom binary number sequence Reviewed

    Yuki Taketa, Yuta Kodera, Shogo Tanida, Takuya Kusaka, Yasuyuki Nogami, Norikazu Takahashi, Satoshi Uehara

    Proceedings of the Seventh International Symposium on Computing and Networking Workshops   394 - 400   2019.11

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    DOI: 10.1109/CANDARW.2019.00074

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    Other Link: https://dblp.uni-trier.de/db/conf/ic-nc/candar2019w.html#TaketaKTKNTU19

  • A damped Newton algorithm for nonnegative matrix factorization based on alpha-divergence Reviewed

    Takehiro Sano, Tsuyoshi Migita, Norikazu Takahashi

    Proceedings of the 2019 6th International Conference on Systems and Informatics   350 - 355   2019.11

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    Authorship:Last author, Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    DOI: 10.1109/ICSAI48974.2019.9010306

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    Other Link: https://dblp.uni-trier.de/db/conf/icsai/icsai2019.html#SanoMT19

  • Reconstruction of CT images using iterative least-squares methods with nonnegative constraint Reviewed

    Hiromasa Kohno, Yuichi Tanji, Ken'ichi Fujimoto, Hiroyuki Kitajima, Yo Horikawa, Norikazu Takahashi

    Journal of Signal Processing   23 ( 2 )   41 - 48   2019.3

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    DOI: 10.2299/jsp.23.41

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  • Band-restricted diagonally dominant matrices: Computational complexity and application Reviewed

    Takahashi Norikazu, Hirata Daiki, Jimbo Shuji, Yamamoto Hiroaki

    Journal of Computer and System Sciences   101   100 - 111   2019.3

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    DOI: 10.1016/j.jcss.2018.10.006

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  • A novel NMF algorithm for detecting clusters in directed networks Reviewed

    Yoshito Usuzaka, Norikazu Takahashi

    Proceedings of the 2019 International Conference on Computing, Networking and Communications   148 - 152   2019.2

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    DOI: 10.1109/ICCNC.2019.8685549

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  • Depth-first search algorithms for finding a generalized Moore graph Reviewed

    Yoshiki Satotani, Norikazu Takahashi

    Proceedings of the 2018 IEEE Region 10 Conference   832 - 837   2018.10

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    DOI: 10.1109/TENCON.2018.8650418

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  • A simple sufficient condition for convergence of projected consensus algorithm Reviewed

    Norikazu Takahashi, Kosuke Kawashima

    IEEE Control Systems Letters   2 ( 3 )   537 - 542   2018.6

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    DOI: 10.1109/LCSYS.2018.2843679

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  • A unified global convergence analysis of multiplicative update rules for nonnegative matrix factorization Reviewed

    Norikazu Takahashi, Jiro Katayama, Masato Seki, Jun’ichi Takeuchi

    Computational Optimization and Applications   71 ( 1 )   1 - 30   2018.3

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer New York LLC  

    Multiplicative update rules are a well-known computational method for nonnegative matrix factorization. Depending on the error measure between two matrices, various types of multiplicative update rules have been proposed so far. However, their convergence properties are not fully understood. This paper provides a sufficient condition for a general multiplicative update rule to have the global convergence property in the sense that any sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the optimization problem. Using this condition, it is proved that many of the existing multiplicative update rules have the global convergence property if they are modified slightly so that all variables take positive values. This paper also proposes new multiplicative update rules based on Kullback–Leibler, Gamma, and Rényi divergences. It is shown that these three rules have the global convergence property if the same modification as above is made.

    DOI: 10.1007/s10589-018-9997-y

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  • Reconstruction of CT images by iterative least squares methods with nonnegative constraint Reviewed

    Hiromasa Kohno, Yuichi Tanji, Ken'ichi Fujimoto, Hiroyuki Kitajima, Yo Horikawa, Norikazu Takahashi

    Proceedings of the 2018 International Symposium on Nonlinear Theory and Its Applications   132 - 135   2018

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  • A distributed algorithm for solving Sandberg-Willson equations Reviewed

    Masaaki Takeuchi, Norikazu Takahashi

    Proceedings of the 2018 International Symposium on Nonlinear Theory and Its Applications   259 - 262   2018

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  • Gauss-Seidel HALS algorithm for nonnegative matrix factorization with sparseness and smoothness constraints Reviewed

    Takumi Kimura, Norikazu Takahashi

    IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences   E100A ( 12 )   2925 - 2935   2017.12

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Institute of Electronics, Information and Communication, Engineers, IEICE  

    Nonnegative Matrix Factorization (NMF) with sparseness and smoothness constraints has attracted increasing attention. When these properties are considered, NMF is usually formulated as an optimization problem in which a linear combination of an approximation error term and some regularization terms must be minimized under the constraint that the factor matrices are nonnegative. In this paper, we focus our attention on the error measure based on the Euclidean distance and propose a new iterative method for solving those optimization problems. The proposed method is based on the Hierarchical Alternating Least Squares (HALS) algorithm developed by Cichocki et al. We first present an example to show that the original HALS algorithm can increase the objective value. We then propose a new algorithm called the Gauss-Seidel HALS algorithm that decreases the objective value monotonically. We also prove that it has the global convergence property in the sense of Zangwill. We finally verify the effectiveness of the proposed algorithm through numerical experiments using synthetic and real data.

    DOI: 10.1587/transfun.E100.A.2925

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  • Derivation of multiplicative update rules for nonnegative matrix factorization with regularization terms Reviewed

    Akihiro Koso, Norikazu Takahashi

    Proceedings of the 2017 International Symposium on Nonlinear Theory and Its Applications   322 - 325   2017.12

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  • Analysis of a pseudo-decentralized discrete-time algorithm for estimating algebraic connectivity of multiagent networks Reviewed

    Tomohisa Urakami, Norikazu Takahashi

    Proceedings of the 2017 International Symposium on Nonlinear Theory and Its Applications   427 - 430   2017.12

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  • Graphs that locally maximize clustering coefficient in the space of graphs with a fixed degree sequence Reviewed

    Tatsuya Fukami, Norikazu Takahashi

    DISCRETE APPLIED MATHEMATICS   217 ( 3 )   525 - 535   2017.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    This paper studies the problem of finding graphs that locally maximize the clustering coefficient in the space of graphs with a fixed degree sequence. Such a graph is characterized by the property that the clustering coefficient cannot be increased, no matter how a single 2-switch is applied. First, an explicit formula for the amount of change in the clustering coefficient of a graph caused by a single 2-switch is given. Next, some classes of graphs with the property stated above are presented. An example of such a graph is the one obtained from a tree by replacing its edges with cliques with the same order. (C) 2016 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.dam.2016.10.002

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  • Maximizing algebraic connectivity in the space of graphs with a fixed number of vertices and edges Reviewed

    Kohnosuke Ogiwara, Tatsuya Fukami, Norikazu Takahashi

    IEEE Transactions on Control of Network Systems   4 ( 2 )   359 - 368   2017

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Institute of Electrical and Electronics Engineers Inc.  

    The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, characterizes the performance of some dynamic processes on networks, such as consensus in multiagent networks, synchronization of coupled oscillators, random walks on graphs, and so on. In a multiagent network, for example, the larger the algebraic connectivity of the graph representing interactions between agents is, the faster the convergence speed of a representative consensus algorithm is. This paper tackles the problem of finding graphs that maximize or locally maximize the algebraic connectivity in the space of graphs with a fixed number of vertices and edges. It is shown that some well-known classes of graphs such as star graphs, cycle graphs, complete bipartite graphs, and circulant graphs are algebraic connectivity maximizers or local maximizers under certain conditions.

    DOI: 10.1109/TCNS.2015.2503561

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  • A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence Reviewed

    Satoshi Nakatsu, Norikazu Takahashi

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   10634   335 - 344   2017

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer Verlag  

    We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.

    DOI: 10.1007/978-3-319-70087-8_36

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  • Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence Reviewed

    Norikazu Takahashi, Masato Seki

    European Signal Processing Conference   2016-   438 - 442   2016.11

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:European Signal Processing Conference, EUSIPCO  

    Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.

    DOI: 10.1109/EUSIPCO.2016.7760286

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  • A fast method for finding the edge to be added to minimize betweenness centrality of a specified vertex Reviewed

    Toshiyuki Namba, Tatsuki Kohno, Norikazu Takahashi

    Proceedings of the 2016 International Symposium on Nonlinear Theory and Its Applications   614 - 617   2016

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  • Extensions of a theorem on algebraic connectivity maximizing graphs Reviewed

    Ryoya Ishii, Norikazu Takahashi

    Proceedings of the 2016 International Symposium on Nonlinear Theory and Its Applications   598 - 601   2016

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  • A New Decentralized Discrete-Time Algorithm for Estimating Algebraic Connectivity of Multiagent Networks Reviewed

    Kento Endo, Norikazu Takahashi

    2016 IEEE ASIA PACIFIC CONFERENCE ON CIRCUITS AND SYSTEMS (APCCAS)   232 - 235   2016

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    Algebraic connectivity of a network, which is defined as the second smallest eigenvalue of the Laplacian matrix, represents how strongly the network is connected. This paper proposes a new decentralized discrete-time algorithm for the estimation of the algebraic connectivity of multiagent networks. The validity of the proposed algorithm is verified by theoretical analysis and numerical experiments.

    DOI: 10.1109/APCCAS.2016.7803941

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  • Multiplicative Update for a Class of Constrained Optimization Problems Related to NMF and Its Global Convergence Reviewed

    Norikazu Takahashi, Masato Seki

    2016 24TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO)   438 - 442   2016

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.

    DOI: 10.1109/EUSIPCO.2016.7760286

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  • Complete multipartite graphs maximize algebraic connectivity in the neighborhood based on 2-switch Reviewed

    Takuro Fujihara, Norikazu Takahashi

    Proceedings of the 2015 International Symposium on Nonlinear Theory and its Applications   285 - 288   2015.12

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  • Global Convergence of a Modified HALS Algorithm for Nonnegative Matrix Factorization Reviewed

    Takumi Kimura, Norikazu Takahashi

    2015 IEEE 6TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP)   21 - 24   2015

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE  

    Hierarchical alternating least squares (HALS) algorithms are efficient computational methods for nonnegative matrix factorization (NMF). Given an initial solution, HALS algorithms update the solution block by block iteratively so that the error decreases monotonically. However, update rules in HALS algorithms are not well-defined. In addition, due to this problem, the convergence of the sequence of solutions to a stationary point cannot be proved theoretically. In this paper, we consider the HALS algorithm for the Frobenius norm-based NMF, and prove that a modified version has the global convergence property in the sense of Zangwill.

    DOI: 10.1109/CAMSAP.2015.7383726

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  • Proposal of a truly decentralized algorithm for estimating algebraic connectivity of multi-agent networks Reviewed

    Kazuma Yamane, Norikazu Takahashi

    Proceedings of the 2015 International Symposium on Nonlinear Theory and its Applications   277 - 280   2015

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  • A generalized sufficient condition for global convergence of modified multiplicative updates for NMF Reviewed

    Norikazu Takahashi, Jiro Katayama, Jun'ichi Takeuchi

    Proceedings of the 2014 International Symposium on Nonlinear Theory and its Applications   44 - 47   2014.9

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  • On graphs that locally maximize algebraic connectivity in the space of graphs with the fixed degree sequence Reviewed

    Takuro Fujihara, Norikazu Takahashi

    Proceedings of the 2014 International Symposium on Nonlinear Theory and its Applications   353 - 356   2014.9

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  • New update rules based on Kullback-Leibler, gamma, and Renyi divergences for nonnegative matrix factorization Reviewed

    Masato Seki, Norikazu Takahashi

    Proceedings of the 2014 International Symposium on Nonlinear Theory and its Applications   48 - 51   2014.9

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  • Global convergence of modified multiplicative updates for nonnegative matrix factorization Reviewed

    Norikazu Takahashi, Ryota Hibi

    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS   57 ( 2 )   417 - 440   2014.3

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    Nonnegative matrix factorization (NMF) is the problem of approximating a given nonnegative matrix by the product of two nonnegative matrices. The multiplicative updates proposed by Lee and Seung are widely used as efficient computational methods for NMF. However, the global convergence of these updates is not formally guaranteed because they are not defined for all pairs of nonnegative matrices. In this paper, we consider slightly modified versions of the original multiplicative updates and study their global convergence properties. The only difference between the modified updates and the original ones is that the former do not allow variables to take values less than a user-specified positive constant. Using Zangwill's global convergence theorem, we prove that any sequence of solutions generated by either of those modified updates has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. Furthermore, we propose algorithms based on the modified updates that always stop within a finite number of iterations.

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  • New classes of clustering coefficient locally maximizing graphs Reviewed

    Tatsuya Fukami, Norikazu Takahashi

    DISCRETE APPLIED MATHEMATICS   162   202 - 213   2014.1

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    A simple connected undirected graph G is called a clustering coefficient locally maximizing graph if its clustering coefficient is not less than that of any simple connected graph obtained from G-by-rewiring an edge, that is, removing an edge and adding a new edge. In this paper, we present some new classes of clustering coefficient locally maximizing graphs. We first show that any graph composed of multiple cliques with orders greater than two sharing one vertex is a clustering coefficient locally maximizing graph. We next show that any graph obtained from a tree by replacing edges with cliques with the same order other than four is a clustering coefficient locally maximizing graph. We also extend the latter result to a more general class. (C) 2013 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.dam.2013.09.013

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  • On Graphs that Locally Maximize Global Clustering Coefficient Reviewed

    Tetsuro Teraji, Norikazu Takahashi

    Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications   130 - 133   2013

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  • Finding Items Associated with Varied Members in A Pairwise Data Stream Reviewed

    Heejae Kim, Norikazu Takahashi, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

    Proceedings of the 16th Korea-Japan Joint Workshop on Algorithms and Computation   52 - 58   2013

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  • Explicit proof of an inequality related to the Omega-matrix Reviewed

    Nishi Tetsuo, Oishi Shin'ichi, Takahashi Norikazu

    Nonlinear Theory and Its Applications, IEICE   4 ( 4 )   430 - 450   2013

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    The authors recently published a paper on some properties of the solution curves for the last n-1 equations of F(x)+Ax=b where x=[x1,x2,...,xn]T is a variable, F(x):Rn → Rn is a nonlinear function of which the first and second derivatives are strictly positive, A ∈ Rn × n is an Ω-matrix, and b ∈ Rn is a constant vector. In that paper, the authors showed that any solution curve possesses neither maximal points nor inflection points with respect to x1, by making use of a fundamental property of Ω-matrices, which is expressed in the form of inequality. However, the proof was a little unclear as shown in Introduction. The objective of this paper is to give an explicit proof for the property of Ω-matrices, which makes the author's previous result more rigorous.

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  • Boundedness of modified multiplicative updates for nonnegative matrix factorization Reviewed

    Jiro Katayama, Norikazu Takahashi, Jun'Ichi Takeuchi

    2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013   252 - 255   2013

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    There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem. © 2013 IEEE.

    DOI: 10.1109/CAMSAP.2013.6714055

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  • A Theorem on a Solution Curve of a Class of Nonlinear Equations

    Tetsuo Nishi, Shin'ichi Oishi, Norikazu Takahashi

    Proceedings of 2012 International Symposium on Nonlinear Theory and its Applications   288 - 291   2012

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  • A Modified Multiplicative Update Algorithm for Convex Quadratic Programming Problems with Nonnegativity Constraints

    Jiro Katayama, Norikazu Takahashi

    Proceedings of 2012 International Symposium on Nonlinear Theory and its Applications   431 - 434   2012

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  • Information Theoretic Limit of Single-Frame Super-Resolution Reviewed

    Kotaro Yamaguchi, Masanori Kawakita, Norikazu Takahashi, Jun'ichi Takeuchi

    2012 THIRD INTERNATIONAL CONFERENCE ON EMERGING SECURITY TECHNOLOGIES (EST)   82 - 85   2012

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    We elucidate the potential limit of single-frame super-resolution by information theory. Though various algorithms for super-resolution have been proposed, there exist only few works that evaluate the performance of super-resolution to our knowledge. Our key idea is that "single-frame super-resolution task can be regarded as channel coding in information theory." Based on this recognition, we can apply some techniques of information theory to the analysis of single-frame super-resolution. As its first step, we clarify the potential limit of single-frame super-resolution. For this purpose, we use a model of Yang et al. (2008) as a statistical model of natural images. As a result, we elucidate the condition that "arbitrary high-resolution natural image can be potentially recovered with arbitrarily small error by single-frame super-resolution." This condition depends on S/N ratio and blurring parameter. We investigate numerically whether this condition is satisfied or not for several situations.

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  • Some properties of solution curves of a class of nonlinear equations and the number of solutions Invited Reviewed

    Nishi Tetsuo, Oishi Shin'ichi, Takahashi Norikazu

    Nonlinear Theory and Its Applications, IEICE   3 ( 3 )   301 - 335   2012

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    This paper gives several theorems on solution curves of a class of nonlinear equations consisting of n variables and (n-1) equations. In particular we give a remarkable theorem on the rank of a Jacobian matrix associated with the above equations. For the proof of these theorems the Ω-matrix, which one of the authors defined previously, and the irreducible matrix play a definitely important role. As the result we show that the solution curves consist of only two types of curves.

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  • A New Continuous-Time Algorithm for Calculating Algebraic Connectivity of Multi-Agent Networks Reviewed

    Tatsuya Fukami, Norikazu Takahashi

    Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications   45 - 48   2012

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  • On Topology of Networked Multi-Agent Systems for Fast Consensus Reviewed

    Kohnosuke Ogiwara, Norikazu Takahashi

    Proceedings of the 2011 International Symposium on Nonlinear Theory and its Applications   56 - 59   2011

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  • Controlling clustering coefficient of graphs by means of 2-switch method Reviewed

    Tatsuya Fukami, Norikazu Takahashi

    Proceedings of 2011 International Symposium on Nonlinear Theory and its Applications   64 - 67   2011

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  • A Modified Multiplicative Update Algorithm for Euclidean Distance-Based Nonnegative Matrix Factorization and Its Global Convergence Reviewed

    Ryota Hibi, Norikazu Takahashi

    NEURAL INFORMATION PROCESSING, PT II   7063   655 - 662   2011

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    Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient computation method for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this paper, we consider NMF in which the approximation error is measured by the Euclidean distance between two matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.

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  • Global Asymptotic Stability of Nonlinear Circuits Related to Maximum Flow Problems Reviewed

    Norikazu Takahashi

    Nonlinear Theory and Its Applications, IEICE   2 ( 4 )   432 - 442   2011

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    Global asymptotic stability of the nonlinear circuit similar to the one proposed by Sato et al. for solving the maximum flow problem is studied in this paper. The circuit consists of two independent DC voltage sources, capacitors and nonlinear resistors. It is proved rigorously that the circuit has a unique equilibrium point which is globally asymptotically stable. From the viewpoint of dynamical systems, the circuit is a cooperative system, and thus some fundamental results concerning the convergence property of cooperative systems play important roles.

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  • Maximum Clustering Coefficient of Graphs with Given Number of Vertices and Edges Reviewed

    Saki Koizuka, Norikazu Takahashi

    Nonlinear Theory and Its Applications, IEICE   2 ( 4 )   443 - 457   2011

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    The clustering coefficient is one of the most important quantities characterizing complex networks. It is often said that many networks in the real world have high clustering coefficients. However, properties of the clustering coefficient itself have not been discussed much in the literature. In this paper, some fundamental properties of the clustering coefficient are studied. First we try to find the maximum value of the clustering coefficient of graphs with the given number of vertices and edges. Next we present some classes of graphs such that each member maximizes the clustering coefficient among its neighbors having the same number of vertices and edges.

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  • Clustering Coefficient Local Maximality of Some Classes of Block Graphs

    Fukami Tatsuya, Takahashi Norikazu

    Record of Joint Conference of Electrical and Electronics Engineers in Kyushu   2011   393 - 393   2011

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    DOI: 10.11527/jceeek.2011.0_393

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  • A Study on Algebraic Connectivity Local Maximality of a Certain Class of Regular Graphs

    Ogiwara Kohnosuke, Takahashi Norikazu

    Record of Joint Conference of Electrical and Electronics Engineers in Kyushu   2011   394 - 395   2011

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    DOI: 10.11527/jceeek.2011.0_394

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  • A Modified Multiplicative Update Algorithm with a Termination Criterion for NMF

    Hibi Ryota, Takahashi Norikazu

    Record of Joint Conference of Electrical and Electronics Engineers in Kyushu   2011   77 - 77   2011

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    DOI: 10.11527/jceeek.2011.0_77

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  • Sufficient conditions for one-dimensional cellular neural networks to perform connected component detection Reviewed

    Norikazu Takahashi, Ken Ishitobi, Tetsuo Nishi

    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS   11 ( 5 )   4202 - 4213   2010.10

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    It is well known that one-dimensional cellular neural networks (1D CNNs) with the template A = [1, 2, -1] can perform connected component detection (CCD). However, this has been confirmed only by numerical and laboratory experiments. In this paper, sufficient conditions for 1D CNNs to perform CCD are obtained through theoretical analysis. Main result shows that a wide class of templates including A = [1, 2, -1] can be used for CCD. (C) 2010 Elsevier Ltd. All rights reserved.

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  • Global Asymptotic Stability Analysis of Nonlinear Circuits for Solving the Maximum Flow Problem

    Norikazu Takahashi

    Proceedings of 2010 International Symposium on Nonlinear Theory and its Applications   358 - 361   2010

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  • Analysis of Signal Propagation in 1-D CNNs with the Antisymmetric Template

    Norikazu Takahashi, Tetsuo Nishi, Hajime Hara

    Proceedings of 12th IEEE International Workshop on Cellular Nanoscale Networks and their Applications   2010

  • A Two-Phase Decomposition Algorithm for Solving Convex Quadratic Programming Problems

    Yuta Kobayashi, Norikazu Takahashi

    Proceedings of 2009 International Symposium on Nonlinear Theory and its Applications   576 - 579   2009

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  • On Clustering Coefficients of Graphs with the Fixed Numbers of Vertices and Edges Reviewed

    Norikazu Takahashi

    2009 EUROPEAN CONFERENCE ON CIRCUIT THEORY AND DESIGN, VOLS 1 AND 2   814 - 817   2009

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    The problem of finding the minimum and maximum values of the clustering coefficients of graphs with the fixed numbers of vertices and edges is considered. It is shown that when a graph has n vertices and the average degree is n/2 the clustering coefficient can take values from 0 to 1 1/2(n 1).

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  • Stable Patterns Realized by a Class of One-Dimensional Two-Layer CNNs Reviewed

    Norikazu Takahashi, Makoto Nagayoshi, Susumu Kawabata, Tetsuo Nishi

    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS   55 ( 11 )   3607 - 3620   2008.12

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    Stable patterns that can be realized by a class of 1-D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple,way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets.

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  • Global convergence of SMO algorithm for support vector regression Reviewed

    Norikazu Takahashi, Jun Guo, Tetsuo Nishi

    IEEE TRANSACTIONS ON NEURAL NETWORKS   19 ( 6 )   971 - 982   2008.6

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    Global convergence of the sequential minimal optimization (SMO) algorithm for support vector regression (SVR) is studied in this paper. Given l training samples, SVR is formulated as a convex quadratic programming (QP) problem with l pairs of variables. We prove that if two pairs of variables violating the optimality condition are chosen for update in each step and subproblems are solved in a certain way, then the SMO algorithm always stops within a finite number of iterations after finding an optimal solution. Also, efficient implementation techniques for the SMO algorithm are presented and compared experimentally with other SMO algorithms.

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  • Stable patterns realized by a class of one-dimensional two-layer CNNs Reviewed

    Norikazu Takahashi, Makoto Nagayoshi, Susumu Kawabata, Tetsuo Nishi

    IEEE Transactions on Circuits and Systems I: Regular Papers   55 ( 11 )   3607 - 3620   2008

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    Stable patterns that can be realized by a class of 1-D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets. © 2008 IEEE.

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  • An Efficient Algorithm for Multi-class Support Vector Machines Reviewed

    Jun Guo, Norikazu Takahashi, Wenxin Hu

    2008 INTERNATIONAL CONFERENCE ON ADVANCED COMPUTER THEORY AND ENGINEERING   327 - +   2008

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    A novel algorithm for multi-class support vector machines (SVMs) is proposed in this paper The tree constructed in our algorithm consists of a series of two-class SVMs. Considering both separability and balance, in each iteration multi-class patterns are divided into two sets according to the distances between pairwise classes and the number of patterns in each class. This algorithm can well treat with the unequally distributed problems. The efficiency of the proposed method are verified by the experimental results.

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  • A new decomposition algorithm for solving convex quadratic programming problems

    TAKAHASHI N.

    Proceedings of 2008 International Symposium on Nonlinear Theory and its Application   73 - 76   2008

  • Global Convergence Analysis of Decomposition Methods for Support Vector Regression Reviewed

    Jun Guo, Norikazu Takahashi

    ADVANCES IN NEURAL NETWORKS - ISNN 2008, PT I, PROCEEDINGS   5263   663 - +   2008

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    Decomposition method has been widely used to efficiently solve the large size quadratic programming (QP) problems arising in support vector regression (SVR). In a decomposition method, a large QP problem is decomposed into a series of smaller QP subproblems, which can be solved much faster than the original one. In this paper, we analyze the global convergence of decomposition methods for SVR. We will show the decomposition methods for the convex programming problem formulated by Flake and Lawrence always stop within a finite number of iterations.

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  • On Asymptotic Behavior of State Trajectories of Piecewise-Linear Recurrent Neural Networks Generating Periodic Sequence of Binary Vectors Reviewed

    Norikazu Takahashi, Yasuhiro Minetoma

    2008 IEEE INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS, VOLS 1-8   484 - 489   2008

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    Recently a sufficient condition for the recurrent neural network with the piecewise-linear output characteristic to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component has been derived. If a recurrent neural network satisfies this condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this paper, we study asymptotic behavior of state trajectories of recurrent neural networks satisfying the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle.

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  • A New Working Set Selection for Decomposition-Type SVM Learning Algorithms

    Norikazu Takahashi, Masashi Kuranoshita, Yusuke Kawazoe, Jun Guo, Jun'ichi Takeuch

    Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications   280 - 283   2007

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  • Sufficient conditions for 1-D CNNs with opposite-sign templates to perform connected component detection Reviewed

    Norikazu Takahashi, Ken Ishitobi, Tetsuo Nishi

    2007 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOLS 1-11   3159 - +   2007

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    Connected component detection (CCD) is an important image processing task done by one-dimensional cellular neural networks (1-D CNNs). Recently, some sufficient conditions for 1-D CNNs with the antisymmetric template A = [s,p, -s] to perform CCD have been derived under the assumption that the outputs of the boundary cells are set to 1 or -1. In this paper, we extend these results to I-D CNNs with the opposite-sign template A = [r,p, -s]. It is shown that the 1-D CNN can perform CCD for a wide range of parameter space. Therefore we can design I-D CNNs which not only can perform CCD but also are robust against small perturbations of the parameters.

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  • A Stability Condition for a Simple Type of Two-Dimensional Discrete-Time Binary Cellular Neural Networks

    Hajime Hara, Tomotaka Ogura, Toshio Asano, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications   19 - 22   2007

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  • Necessary and sufficient conditions for one-dimensional discrete-time autonomous binary cellular neural networks to be stable Reviewed

    Tetsuo Nishi, Norikazu Takahashi, Hajime Hara

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E89A ( 12 )   3693 - 3698   2006.12

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    We give the necessary and sufficient conditions for a one-dimensional discrete-time autonomous binary cellular neural networks to be stable in the case of fixed boundary. The results are complete generalization of our previous one [16] in which the symmetrical connections were assumed. The conditions are compared with some stability conditions so far known.

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  • Global convergence of decomposition learning methods for support vector machines Reviewed

    Norikazu Takahashi, Tetsuo Nishi

    IEEE TRANSACTIONS ON NEURAL NETWORKS   17 ( 6 )   1362 - 1369   2006.11

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    Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required,. decomposition methods are applicable to large QP problems. In this paper,. We will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables.

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  • Necessary and sufficient conditions for a 1-D DBCNN with an input to be stable in terms of connection coefficients Reviewed

    Tetsuo Nishi, Hajime Hara, Norikazu Takahashi

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E89A ( 10 )   2825 - 2832   2006.10

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    We give necessary and sufficient conditions for a I-D DBCNN (1-dimensional discrete-time binary cellular neural network) with an external input to be stable in terms of connection coefficients. The results are generalization of our previous one [18], [19] in which the input was assumed to be zero.

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  • An efficient method for simplifying decision functions of support vector machines Reviewed

    Jun Guo, Norikazu Takahashi, Tetsuo Nishi

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E89A ( 10 )   2795 - 2802   2006.10

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    A novel method to simplify decision functions of support vector machines (SVMs) is proposed in this paper. In our method, a decision function is determined first in a usual way by using all training samples. Next those support vectors which contribute less to the decision function are excluded from the training samples. Finally a new decision function is obtained by using the remaining samples. Experimental results show that the proposed method can effectively simplify decision functions of SVMs without reducing the generalization capability.

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  • Necessary and sufficient condition for a class of planar dynamical systems related to CNNs to be completely stable Reviewed

    Norikazu Takahashi, Tetsuo Nishi

    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS   53 ( 8 )   727 - 733   2006.8

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    We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.

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  • A novel sequential minimal optimization algorithm for support vector regression Reviewed

    Jun Guo, Norikazu Takahashi, Tetsuo Nishi

    NEURAL INFORMATION PROCESSING, PT 1, PROCEEDINGS   4232   827 - 836   2006

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    A novel sequential minimal optimization (SMO) algorithm for support vector regression is proposed. This algorithm is based on Flake and Lawrence's SMO in which convex optimization problems with iota variables are solved instead of standard quadratic programming problems with 2 iota variables where iota is the number of training samples, but the strategy for working set selection is quite different. Experimental results show that the proposed algorithm is much faster than Flake and Lawrence's SMO and comparable to the fastest conventional SMO.

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  • Study on the Number of Equilibrium Points for a 1-D DBCNN with No Input

    Hajime Hara, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications   727 - 730   2006

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  • Further Analysis on Condition for 1-D CNNs to Perform Connected Component Detection

    Norikazu Takahashi, Tetsuo Nishi

    Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications   735 - 738   2006

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  • Convergence proof of a sequential minimal optimization algorithm for support vector regression Reviewed

    Jun Guo, Norikazu Takahashi, Tetsuo Nishi

    2006 IEEE INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORK PROCEEDINGS, VOLS 1-10   355 - +   2006

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    A sequential minimal optimization (SMO) algorithm for support vector regression (SVR) has recently been proposed by Flake and Lawrence. However, the convergence of their algorithm has not been proved so far. In this paper, we consider an SMO algorithm, which deals with the same optimization problem as Flake and Lawrence's SMO, and give a rigorous proof that it always stops within a finite number of iterations.

    DOI: 10.1109/IJCNN.2006.246703

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  • A sufficient condition for 1-D CNNs with antisymmetric templates to perform connected component detection Reviewed

    Norikazu Takahashi, Tetsuo Nishi

    2006 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOLS 1-11, PROCEEDINGS   2169 - 2172   2006

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    Global dynamical behavior of one-dimensional cellular neural networks (1-D CNNs) with the antisymmetric template A = [s, p, -s] is studied in this paper. Under the assumption that the outputs of the boundary cells are fixed to 1 or -1, a new sufficient condition for such CNNs to perform connected component detection will be presented.

    DOI: 10.1109/ISCAS.2006.1693048

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  • Rigorous proof of termination of SMO algorithm for support vector machines

    N Takahashi, T Nishi

    IEEE TRANSACTIONS ON NEURAL NETWORKS   16 ( 3 )   774 - 776   2005.5

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    Sequential minimal optimization (SMO) algorithm is one of the simplest decomposition methods for learning of support vector machines (SVMs). Keerthi and Gilbert have recently studied the convergence property of SMO algorithm and given a proof that SMO algorithm always stops within a finite number of iterations. In this letter, we point out the incompleteness of their proof and give a more rigorous proof.

    DOI: 10.1109/TNN.2005.844857

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  • A learning algorithm for enhancing the generalization ability of support vector machines

    J Guo, N Takahashi, T Nishi

    2005 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS), VOLS 1-6, CONFERENCE PROCEEDINGS   3631 - 3634   2005

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    We propose an innovative learning algorithm for enhancing the generalization ability of support vector machines (SVMs), when the Gausssian radial basis function (RBF) is used and when the parameter sigma, is very small. As learning patterns it uses not only the prescribed learning patterns but also newly inserted patterns in their neighbourhoods. In spite of the inserted many patterns, the size of the proposed optimization problem can be reduced to be same as the original one by using the averaging method. Many simulation results show the effectiveness of the proposed algorithm.

    DOI: 10.1109/ISCAS.2005.1465416

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  • A learning algorithm for enhancing the generalization ability of support vector machines Reviewed

    Jun Guo, Norikazu Takahashi, Tetsuo Nishi

    Proceedings - IEEE International Symposium on Circuits and Systems   3631 - 3634   2005

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    We propose an innovative learning algorithm for enhancing the generalization ability of support vector machines (SVMs), when the Gausssian radial basis function (RBF) is used and when the parameter σ is very small. As learning patterns it uses not only the prescribed learning patterns but also newly inserted patterns in their neighbourhoods. In spite of the inserted many patterns, the size of the proposed optimization problem can be reduced to be same as the original one by using the averaging method. Many simulation results show the effectiveness of the proposed algorithm. © 2005 IEEE.

    DOI: 10.1109/ISCAS.2005.1465416

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  • Realization of limit cycles by neural networks with piecewise linear activation function

    N Takahashi, T Yamakawa, T Nishi

    PROCEEDINGS OF THE 2005 EUROPEAN CONFERENCE ON CIRCUIT THEORY AND DESIGN, VOL 3   7 - 10   2005

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    A simple method of realizing a prescribed limit cycle by means of a continuous-time recurrent neural network with the piecewise-linear activation function is proposed. Since the proposed method is formulated as a set of linear inequalities, we can easily determine parameters of the network by using, for example, the simplex method.

    DOI: 10.1109/ECCTD.2005.1523047

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  • On complete stability of three-Cell CNNs with opposite-sign templates Reviewed

    Norikazu Takahashi, Tetsuo Nishi

    Proceedings - IEEE International Symposium on Circuits and Systems   4673 - 4676   2005

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    A new sufficient condition for three-cell cellular neural networks (CNNs) with the opposite-sign template to be completely stable is presented in this paper. It is also shown that even though the self-coupling is greater than unity the state trajectory which never enters a total saturation region can exist. © 2005 IEEE.

    DOI: 10.1109/ISCAS.2005.1465675

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  • On complete stability of three-cell CNNs with opposite-sign templates

    N Takahashi, T Nishi

    2005 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS), VOLS 1-6, CONFERENCE PROCEEDINGS   4673 - 4676   2005

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    A new sufficient condition for three-cell cellular neural networks (CNNs) with the opposite-sign template to be completely stable is presented in this paper. It is also shown that even though the self-coupling is greater than unity the state trajectory which never enters a total saturation region can exist.

    DOI: 10.1109/ISCAS.2005.1465675

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  • An Efficient Method for Searching Optimal Kernel Parameter of Support Vector Machines

    Keisuke Arima, Norikazu Takahashi

    Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications   238 - 241   2005

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  • A learning algorithm for improving the classification speed of support vector machines

    J Guo, N Takahashi, T Nishi

    PROCEEDINGS OF THE 2005 EUROPEAN CONFERENCE ON CIRCUIT THEORY AND DESIGN, VOL 3   381 - 384   2005

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    A novel method for training support vector machines (SVMs) is proposed to speed up the SVMs in test phase. It has three main steps. First, an SVM is trained on all the training samples, thereby producing a number of support vectors. Second, the support vectors, which contribute less to the shape of the decision surface, are excluded from the training set. Finally, the SVM is re-trained only on the remaining samples. Compared to the initially trained SVM, the efficiency of the finally trained SVM is highly improved, without system degradation.

    DOI: 10.1109/ECCTD.2005.1523140

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  • Necessary and sufficient conditions for 2-dimensional discrete-time systems described by the signum function to be stable

    H Hara, T Nishii, N Takahashi

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E87A ( 6 )   1500 - 1502   2004.6

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    In this paper we give the necessary and sufficient conditions for 2-dimensional discrete-time systems described by the signum function to be stable.

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  • Realization of Limit Cycles with Length 8 or 4 by Three-Dimensional Binary State Equations

    Hajime Hara, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of 2004 International Technical Conference on Circuits/Systems, Computers and Communications   7B2L-4-1-7B2L-4-4   2004

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  • Necessary and sufficient conditions for one-dimensional discrete-time binary cellular neural network to be stable-No input case

    NISHI T.

    Proc. 8th IEEE International Biannual Workshop on Cellular Neural Networks and their Applications, Budapest, Hungary, July 2004   453 - 458   2004

  • On stable patterns realized by a class of one-dimensional two-layer CNNs

    M Nagayoshi, N Takahashi, T Nishi

    2004 47TH MIDWEST SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL I, CONFERENCE PROCEEDINGS   1   385 - 388   2004

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    This paper presents some properties of stable patterns that can be realized by a certain type of one-dimensional two-layer cellular neural networks (CNNs). We first introduce a notion of admissible local pattern (ALP) set. All the stable patterns of a CNN can be completely determined by the ALP set. We next show that all of 256 possible ALP sets can be realized by twolayer CNNs, while only 59 can be realized by single-layer CNNs. This means two-layer CNNs have a much higher potential for signal processing than single-layer CNNs.

    DOI: 10.1109/MWSCAS.2004.1354008

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  • Necessary and Sufficient Conditions for One-Dimensional Discrete-Time Binary Cellular Neural Network

    Hajime Hara, Norikazu Takahashi, Tetsuo Nishi

    Proceedings of 2004 IEEE International Midwest Symposium on Circuits and Systems   1   389 - 392   2004

  • Global convergence analysis of decomposition methods for support vector machines

    N Takahashi, T Nishi

    2004 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL 5, PROCEEDINGS   5   728 - 731   2004

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    Convergence property of decomposition methods for solving quadratic optimization problems arising in support vector machines is studied. It is shown that under a mild condition any decomposition method converges to an optimal solution.

    DOI: 10.1109/ISCAS.2004.1329911

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  • An Efficient Decomposition Learning Method for Support Vector Regression

    Masashi Kuranoshita, Norikazu Takahashi, Tetsuo Nishi

    Proceedings of 2004 International Symposium on Nonlinear Theory and its Applications   705 - 708   2004

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  • A Design Method of Cellular Neural Networks for Associative Memories based on Linear Programming

    Tsuyoshi Yamakawa, Norikazu Takahashi, Tetsuo Nishi

    Proceedings of 2004 International Symposium on Nonlinear Theory and its Applications   641 - 644   2004

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  • A Learning Method for Robust Support Vector Machines

    Jun Guo, Norikazu Takahashi, Tetsuo Nishi

    Proceedings of 2004 International Symposium on Neural Networks   474 - 479   2004

  • An improvement of the design method of cellular neural networks based on generalized eigenvalue minimization

    R Bise, N Takahashi, T Nishi

    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS   50 ( 12 )   1569 - 1574   2003.12

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    Realization of associative memories by cellular neural networks (CNNs) with binary output is studied. Concerning this problem, a CNN design method based upon generalized eigenvalue minimization (GEVM) has recently been proposed. In this brief, a new CNN design method which is based on the GEVM-based method will be presented. We first give some analytical results related to the basin of attraction of a memory vector. We then derive the design method by combining these analytical results and the GEVM-based method. We finally show through computer simulations that the proposed method can achieve higher recall probability than the original GEVM-based method.

    DOI: 10.1109/TCSI.2003.819827

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  • An improvement of the design method of cellular neural networks based on generalized eigenvalue minimization Reviewed

    Ryoma Bise, Norikazu Takahashi, Tetsuo Nishi

    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications   50 ( 12 )   1569 - 1574   2003.12

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    Realization of associative memories by cellular neural networks (CNNs) with binary output is studied. Concerning this problem, a CNN design method based upon generalized eigenvalue minimization (GEVM) has recently been proposed. In this brief, a new CNN design method which is based on the GEVM-based method will be presented. We first give some analytical results related to the basin of attraction of a memory vector. We then derive the design method by combining these analytical results and the GEVM-based method. We finally show through computer simulations that the proposed method can achieve higher recall probability than the original GEVM-based method.

    DOI: 10.1109/TCSI.2003.819827

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  • A method for solving optimization problems with equality constraints by using the SPICE program

    J Guo, T Nishi, N Takahashi

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E86A ( 9 )   2325 - 2332   2003.9

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    Analog Hopfield neural networks (HNNs) have so far been used to solve many kinds of optimization problems, in particular, combinatorial problems such as the TSP, which call be described by an objective function and some equality constraints. When we solve a minimization problem with equality constraints by using HNNs, however, the constraints are satisfied only approximately. In this paper we propose a circuit which rigorously realizes the equality constraints and whose energy function corresponds to the prescribed objective function. We use the SPICE program to solve circuit equations corresponding to the above circuits. The proposed method is applied to several kinds of optimization problems and the results are very satisfactory.

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  • Effect of Biases on the Complete Stability of Planar Dynamical Systems related to CNNs

    Norikazu Takahashi, Tetsuo Nishi

    Proceedings of the 2003 Workshop on Nonlinear Dynamics of Electronic Systems   263 - 266   2003

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  • An Analog Circuit for Solving a kind of Constrained Optimization Problems

    Jun Guo, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of 2003 International Symposium on Intelligent Signal Processing and Communication Systems   192 - 197   2003

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  • A Consideration on the Stability of the Third-Order Discrete-Time Systems Including Signum Function

    Hajime Hara, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of International Symposium on Information Science and Electrical Engineering 2003   22 - 25   2003

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  • On Termination of SMO Algorithm for Support Vector Machines

    Norikazu Takahashi, Tetsuo Nishi

    Proceedings of International Symposium on Information Science and Electrical Engineering 2003   187 - 190   2003

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  • Necessary and Sufficient Condition for the Second-Order Discrete-Time Systems Described by the Signum Function to be Stable

    Hajime Hara, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of the 2003 International Technical Conference on Circuits, Systems, Computers and Communications   585 - 588   2003

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  • A generalization of some complete stability conditions for cellular neural networks with delay

    N Takahashi, T Nishi

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E85A ( 9 )   2044 - 2051   2002.9

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    This paper gives a new sufficient condition for cellular neural networks with delay (DCNNs) to be completely stable. The result is a generalization of two existing stability conditions for DCNNs, and also contains a complete stability condition for standard CNNs as a special case. Our new sufficient condition does not require the uniqueness of equilibrium point of DCNNs and is independent of the length of delay.

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  • Necessary and sufficient conditions for one-dimensional discrete-time binary cellular neural networks with unspecified fixed boundaries to be stable

    H Sato, T Nishi, N Takahashi

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E85A ( 9 )   2036 - 2043   2002.9

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    This paper investigates the behavior of one-dimensional discrete-time binary cellular neural networks with both the A- and B-templates and gives the necessary and sufficient conditions for the above network to be stable for unspecified fixed boundaries.

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  • One-dimensional Discrete-time Binary Cellular Neural Networks and Some Examples for Signal Processing

    SATO Hidenori, NISHI Tetsuo, TAKAHASHI Norikazu

    Research reports on information science and electrical engineering of Kyushu University   7 ( 2 )   93 - 98   2002.9

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    DOI: 10.15017/1525450

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    Other Link: http://hdl.handle.net/2324/1525450

  • Associative Memory with Hidden Units by a Hybrid Learning

    Jun Tsuzurugi, Norikazu Takahashi, Shin Ishii

    Transactions of the Institute of Systems, Control and Information Engineers   15 ( 11 )   600 - 606   2002

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    Publishing type:Research paper (scientific journal)   Publisher:The Institute of Systems, Control and Information Engineers  

    DOI: 10.5687/iscie.15.600

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  • On the design method of cellular neural networks for associative memories based on generalized eigenvalue problem Reviewed

    R Bise, N Takahashi, T Nishi

    CELLULAR NEURAL NETWORKS AND THEIR APPLICATIONS   515 - 522   2002

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    This paper presents a design technique which is used to realize associative memories via cellular neural networks. The proposed method can store every prototype vector as a memory vector and maximize the areas of basin of attraction of memory vectors in a certain sense. The network parameters are obtained by solving optimization problems known as generalized eigenvalue problems. Simulation results proves that our method is better than the existing ones.

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  • Necessary and Sufficient Condition for Two-Cell CNNs with Space-Invariant Connections to be Globally Stable

    Norikazu Takahashi, Tetsuo Nishi

    Proceedings of 2002 International Symposium on Nonlinear Theory and its Applications   611 - 614   2002

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  • Necessary and sufficient conditions for one-dimensional discrete-time binary cellular neural networks with both A- and B-templates to be stable

    Tetsuo Nishi, Hidenori Sato, Norikazu Takahashi

    Proceedings - IEEE International Symposium on Circuits and Systems   1   633 - 636   2002

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    We give the necessary and sufficient conditions for a one-dimensional discrete-time binary cellular neural networks with both the A- and B-templates to be stable for a fixed boundary.

    DOI: 10.1109/ISCAS.2002.1009920

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  • One-dimensional Discrete-time Binary Cellular Neural Networks with A- and B-templates

    Hidenori Sato, Tetsuo Nishi, Norikazu Takahashi

    Proceedings of 2001 International Symposium on Nonlinear Theory and its Applications   1   51 - 54   2001

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  • A new sufficient condition for complete stability of cellular neural networks with delay

    N Takahashi

    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS   47 ( 6 )   793 - 799   2000.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

    DOI: 10.1109/81.852931

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  • On the complete stability of nonsymmetric cellular neural networks

    N Takahashi, LO Chua

    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS   45 ( 7 )   754 - 758   1998.7

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    This paper gives a new sufficient condition for complete stability of a nonsymmetric cellular neural network (CNN). The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in our proof. It is also shown that the existence of a stable equilibrium point does not imply complete stability of a nonsymmetric CNN.

    DOI: 10.1109/81.703843

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  • A test for nonnegativity of real polynomials Reviewed

    T Nishi, N Takahashi

    ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE   81 ( 5 )   58 - 65   1998.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SCRIPTA TECHNICA-JOHN WILEY & SONS  

    A rigorous method to determine whether a polynomial f(x) is nonnegative for all x in an interval is proposed, Conventionally, a method which determines whether the multiplicity of every zero of f(x) is even has been used for this problem. The conventional method is, however, somewhat complicated because the Sturm function sequence must be generated repeatedly and the number of variations of sign must be investigated for each sequence. The method proposed in this paper determines whether f(x) + epsilon (epsilon is a sufficiently small positive number) is positive for all x in the interval. This method is simpler than the conventional one in the sense that only two Sturm function sequences art. generated. Moreover, the determination can easily be made with the number of variations of sign of the function sequence made by concatenating two Sturm function sequences. (C) 1998 Scripta Technica.

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  • A new sufficient condition for nonsymmetric CNN's to have a stable equilibrium point

    N Takahashi, LO Chua

    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS   44 ( 11 )   1092 - 1095   1997.11

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    This letter gives a new sufficient condition for nonsymmetric CNN's to have at least one stable equilibrium point. Existence of a stable equilibrium point is important for nonsymmetric CNN's because it is a necessary condition for complete stability. It is shown that our sufficient condition is a generalization of a previous result concerning the existence of a stable equilibrium point, and that it can easily be applied to space-invariant CNN's with a 3 x 3 neighborhood.

    DOI: 10.1109/81.641777

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  • The Number of Equilibrium Points and Their Basins of Attraction of Neural Networks with a Kind of Cyclic Connection Matrix

    TAKAHASHI Norikazu, NISHI Tetsuo

    Research reports on information science and electrical engineering of Kyushu University   1 ( 1 )   101 - 104   1996.9

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  • A Test for Nonnegativity of Real Polynomials

    Tetsuo Nishi, Norikazu Takahashi

    The Transactions of the Institute of Electronics, Information and Communication Enigneers A   J79-A ( 4 )   930 - 936   1996

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  • 実係数をもつ多項式の非負値性の判定法

    西哲生, 高橋規一

    電子情報通信学会誌A   J79-A ( 4 )   930 - 936   1996

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  • ON THE NUMBER OF SOLUTIONS OF A CLASS OF NONLINEAR EQUATIONS RELATED TO NEURAL NETWORKS WITH TAPERED CONNECTIONS

    T NISHI, N TAKAHASHI

    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES   E78A ( 10 )   1299 - 1305   1995.10

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    The number of solutions of a nonlinear equation x = sgn(Wx) is discussed. The equation is derived for the determination of equilibrium points of a kind of Hopfield neural networks. We impose some conditions on W. The conditions correspond to the case where a Hopfield neural network has n neurons arranged on a ring, each neuron has connections only from k preceding neurons and the magnitude of k connections decrease as the distance between two neurons increases. We show that the maximum number of solutions for the above case is extremely few and is independent of the number of neurons, n, if k is less than or equal to 4. We also show that the number of solutions generally increases exponentially with n by considering the case where k = n - 1.

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  • 電気回路ハンドブック

    朝倉書店  2016 

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  • Speeding up an algorithm for searching generalized Moore graphs

    平山拓, 右田剛史, 高橋規一

    電子情報通信学会技術研究報告   122 ( 65 )   52 - 57   2022.6

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  • Visualization of decisions of CNN models trained on map images labeled based on traffic accident data

    荒瀬快斗, WU Zhijian, 右田剛史, 高橋規一

    電子情報通信学会技術研究報告   122 ( 65 )   46 - 51   2022.6

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  • Performance evaluation of distributed principal component analysis algorithm based on power method and average consensus

    Mutsuki Oura, Tsuyoshi Migita, Norikazu Takahashi

    1 - 2   2021.10

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  • Deep learning of map Images for prediction of traffic accident hazard areas

    Zhijian Wu, Tsuyoshi Migita, Norikazu Takahashi

    1 - 2   2021.10

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  • Proposal of a method of sending/receiving parameter values in distributed learning of multi-neural networks

    Tatsuya Kayatani, Tsuyoshi Migita, Norikazu Takahashi

    1 - 2   2021.10

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  • Modification of optimization problem in randomized NMF and design of optimization method based on HALS algorithm

    舛田昂生, 右田剛史, 高橋規一

    電子情報通信学会技術研究報告   121 ( 80 )   23 - 30   2021.6

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  • Simplification of average consensus algorithm in distributed HALS algorithm for NMF

    林京寿, 右田剛史, 高橋規一

    電子情報通信学会技術研究報告   121 ( 80 )   15 - 22   2021.6

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  • Graph structure optimization using genetic algorithms

    田尻紘生, 右田剛史, 高橋規一

    電子情報通信学会技術研究報告   120 ( 430 )   23 - 28   2021.3

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  • Proposal of novel distributed learning algorithms for multi-neural networks

    原田和明, 右田剛史, 高橋規一

    電子情報通信学会技術研究報告   120 ( 430 )   17 - 22   2021.3

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  • A step-by-step super-resolution model using edge and grayscale images

    Daiki Hirata, Norikazu Takahashi

    14 - 14   2021.3

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  • Generalization of pseudo-decentralized continuous-time algorithms for estimating algebraic connectivity

    Katsuki Shimada, Tsuyoshi Migita, Norikazu Takahashi

    電子情報通信学会技術研究報告   120 ( 246 )   22 - 27   2020.11

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  • Distributed algorithms based on multiplicative update rules for nonnegative matrix factorization

    Yohei Domen, Tsuyoshi Migita, Norikazu Takahashi

    電子情報通信学会技術研究報告   120 ( 246 )   28 - 33   2020.11

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  • Element-wise alternating least squares algorithm for nonnegative matrix factorization on one-hot encoded data

    Zhuo Wu, Tsuyoshi Migita, Norikazu Takahashi

    1 - 2   2020.10

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  • A novel hierarchical alternating least squares algorithm for L1 regularized nonnegative matrix factorization

    Takehiro Sano, Tsuyoshi Migita, Norikazu Takahashi

    第19回情報科学技術フォーラム講演論文集,第2分冊   173 - 174   2020.8

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  • Performance evaluation of GNMF-based clustering using cluster ensembles Reviewed

    Takehiro Sano, Tsuyoshi Migita, Norikazu Takahashi

    2020年度人工知能学会全国大会(第34回)論文集   1 - 4   2020.6

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  • A genetic algorithm for minimizing average shortest path length of regular graphs

    Reiji Hayashi, Tsuyoshi Migita, Norikazu Takahashi

    120 ( 26 )   11 - 16   2020.5

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  • Design of a distributed algorithm for principal component analysis based on power method and average consensus

    Mutsuki Oura, Tsuyoshi Migita, Norikazu Takahashi

    120 ( 26 )   17 - 22   2020.5

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  • A projected consensus-based algorithm for minimizing the maximum error of a system of linear equations with nonnegativity constraints

    Kosuke Kawashima, Tsuyoshi Migita, Norikazu Takahashi

    電子情報通信学会技術研究報告   119 ( 471 )   19 - 23   2020.3

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  • A distributed algorithm for solving Sandberg-Willson equations based on sequential minimization of convex quadratic functions

    Masaaki Takeuchi, Tsuyoshi Migita, Norikazu Takahashi

    電子情報通信学会技術研究報告   119 ( 471 )   13 - 18   2020.3

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  • Modified multiplicative update rule for GNMF and its global convergence

    Takehiro Sano, Tsuyoshi Migita, Norikazu Takahashi

    138 - 138   2020.3

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  • Merging classifiers CNNs with hierarchized fully connected layer

    Daiki Hirata, Norikazu Takahashi

    11 - 11   2020.3

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  • マイコン実装したAES暗号に対するニューラルネットワークを用いた最終ラウンド鍵の解析—Analyzing Final Round Key of AES Implemented on Microcomputer using Neural Network—情報セキュリティ

    小杉 聡志, 城市 翔, 生田 健, 日下 卓也, 野上 保之, 高橋 規一

    電子情報通信学会技術研究報告 = IEICE technical report : 信学技報   118 ( 478 )   71 - 76   2019.3

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  • Analyzing Final Round Key of AES Implemented on Microcomputer using Neural Network

    小杉聡志, 城市翔, 生田健, 日下卓也, 野上保之, 高橋規一

    電子情報通信学会技術研究報告   118 ( 478(ISEC2018 81-134) )   2019

  • マルチエージェントネットワークによる非負値行列因子分解の分散計算

    道免陽平, 右田剛史, 高橋規一

    情報科学技術フォーラム講演論文集   18th   2019

  • 光源の異なる画像を用いた楕円体と一葉双曲面のパラメータ推定

    那須巧海, 右田剛史, 尺長健, 高橋規一

    情報科学技術フォーラム講演論文集   18th   2019

  • 遺伝アルゴリズムによる代数的連結度最大化

    田尻紘生, 右田剛史, 高橋規一

    情報科学技術フォーラム講演論文集   18th   2019

  • ニューラルネットワークの分散学習における新たな合意重み決定法

    原田和明, 右田剛史, 高橋規一

    情報科学技術フォーラム講演論文集   18th   2019

  • 単調方程式のニュートン型解法に基づく新たな非負値行列因子分解アルゴリズム

    佐野雄大, 右田剛史, 高橋規一

    情報科学技術フォーラム講演論文集   18th   2019

  • Image Reconstruction by Nonnegative Matrix Factorization

    117 ( 225 )   55 - 58   2017.10

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  • Derivation of Global Clustering Coefficient Maximizing Graphs in the Case Where the Size is Close to the Order

    117 ( 225 )   69 - 74   2017.10

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  • A Newton-Type Algorithm for Nonnegative Matrix Factorization with Alpha-Divergence

    117 ( 121 )   17 - 22   2017.7

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  • A Pseudo-Decentralized Discrete-Time Algorithm for Estimating Algebraic Connectivity of Multiagent Networks

    117 ( 18 )   57 - 62   2017.5

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  • Multiplicative Update Rules for Nonnegative Matrix Factorization with Regularization Terms

    117 ( 18 )   63 - 68   2017.5

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  • A New Iterative Method for Nonnegative Matrix Factorization with Sparseness and Smoothness Constraints and Its Global Convergence

    116 ( 395 )   273 - 278   2017.1

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  • Performance Evaluation of a Streaming Algorithm for Detecting Items with the Frequency of Appearance Changing Abruptly

    116 ( 394 )   183 - 188   2017.1

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  • A Fast Method for Finding the Edge to be Inserted to Minimize Betweenness Centrality of a Specified Vertex

    116 ( 215 )   63 - 68   2016.9

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  • A Consideration on Complete Multipartite Graphs that Maximize the Algebraic Connectivity over All Graphs with the Same Number of Vertices and Edges

    116 ( 215 )   51 - 56   2016.9

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  • DS-2-6 STREAMING ALGORITHM TO DETECT ITEMS OF WHICH THE FREQUENCY OF APPEARANCE ABRUPTLY CHANGES

    Kinoshita Tsuyoshi, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2016 ( 1 )   "S - 22"-"S-23"   2016.3

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  • Maximality of the Algebraic Connectivity of Complete Multipartite Graphs and a 2-Switch-Based Method for Finding Algebraic Connectivity Locally Maximizing Graphs

    115 ( 442 )   31 - 36   2016.1

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  • Multiplicative Update for Nonnegative Matrix Factorization based on Generalized Error Function and Its Global Convergence

    115 ( 394 )   67 - 72   2016.1

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  • Derivation of Multiplicative Update for Constrained Optimization Problems Related to NMF and Its Global Convergence Analysis

    115 ( 240 )   21 - 26   2015.10

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  • Proposal of a Truly Distributed Algorithm for Estimating Algebraic Connectivity of Multi-Agent Network

    115 ( 77 )   91 - 96   2015.6

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  • Methods of Generating Regular Graphs with Short Average Path Length

    FUJITA Keisuke, TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   114 ( 484 )   7 - 12   2015.3

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    The problem of finding a regular graph with given number of vertices and given degree that minimizes the average path length is studied. For example, if all terminals in a multi-hop wireless network have the same number of communication channels, the transmission rate in the network depends strongly on the average path length of the regular graph representing the connections between terminals. An important theoretical result related to this problem is the lower bound for the average path length derived by Cerf et al. In this report, we propose some methods of generating automatically regular graphs with short average path length, and examine their effectiveness numerically. It is shown that the lower bound of Cerf et al. is achieved by the proposed methods for some cases.

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  • A-4-8 MODIFICATION OF HIERARCHICAL ALTERNATING LEAST SQUARES METHOD FOR NONNEGATIVE MATRIX FACTORIZATION AND ITS GLOBAL CONVERGENCE

    Kimura Takumi, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2015   95 - 95   2015.2

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  • A-12-1 COMPLETE MULTI-PARTITE GRAPHS AS LOCAL MAXIMIZERS OF THE ALGEBRAIC CONNECTIVITY

    Fujihara Takuro, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2015   173 - 173   2015.2

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  • D-1-12 A POLYNOMIAL TIME ALGORITHM TO CHECK A CONVERGENCE CONDITION FOR DISCRETE-TIME BINARY-VALUED NEURAL NETWORKS

    Hirata Daiki, Takahashi Norikazu, Jimbo Shuji, Yamamoto Hiroaki

    Proceedings of the IEICE General Conference   2015 ( 1 )   12 - 12   2015.2

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  • Derivation of New Update Rules based on KL, γ, Renyi Divergences for Nonnegative Matrix Factorization

    SEKI Masato, TAKAHASHI Norikazu

    Mathematical Systems Science and its Applications : IEICE technical report   114 ( 125 )   253 - 258   2014.7

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    Three new update rules based on Kullback-Leibler divergence, γ-divergence and Renyi divergence for nonnegative matrix factorization are presented in this report. Multiplicative update rules based on these divergences have already been proposed by Yang and Oja. However, their error functions have a common problem that we can increase the values of variables as much as we want while keeping the value of the error function fixed. In addition, the global convergence of their multiplicative update rules is not guaranteed. In order to solve these problems, we add a penalty term to each of the original error functions, and derive three new update rules based on the method of Yang and Oja and the one of Gillis and Glineur. We also prove that the new update rules have the boundedness property which means that any sequence of solutions generated by the new update rules is contained in a bounded region.

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  • A 2-switch-based Method for Searching Algebraic Connectivity Maximizing Graphs and its Application to 3-Regular Graphs

    FUJIHARA Takuro, TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   114 ( 55 )   19 - 24   2014.5

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    How to reach a consensus is an important problem in multiagent networks. In a representative consensus protocol proposed by Olfati-Saber and Murray, the state value of each agent in a network varies with time depending on those of other agents, and eventually converges to the average of the initial state values. The speed of convergence of this protocol is determined by the second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, of the graph representing interactions between agents. In this report, we address the problem of finding a graph that has not only the same degree sequence as a given graph but also the maximum algebraic connectivity among all graphs with the same degree sequence. For this problem, we first propose a local search algorithm based on 2-switch. We then apply this algorithm to 3-regular graphs and investigate the structural characteristics of the obtained graphs.

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  • A consideration on the maximum value of the condition number of matrices

    NISHI Tetsuo, Rump Siegfried M., TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   113 ( 486 )   85 - 90   2014.3

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    An upper bound of the condition number of integer matrices of which elements has magnitude less or equal to a positive integer is investigated. This paper shows the possibility that the upper bound by Guggenheimer et al may be attainable.

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  • A-2-1 ALGEBRAIC CONNECTIVITY LOCALLY MAXIMIZING GRAPHS IN A FAMILY OF GRAPHS WITH THE SAME DEGREE SEQUENCE : THE CASE OF COMPLETE BIPARTITE GRAPHS

    Fujihara Takuro, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2014   26 - 26   2014.3

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  • D-1-8 AN ALGORITHM TO CHECK CONVERGENCE CONDITION FOR DISCRETE-TIME BINARY-VALUED NEURAL NETWORKS

    Hirata Daiki, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2014 ( 1 )   8 - 8   2014.3

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  • A Note on Systematic Construction of Ω-matrices

    TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report. Nonlinear problems   113 ( 271 )   193 - 198   2013.10

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    In 1991, Nishi and Kawane introduced the notion of SZ-matrix in their analysis of DC operating points of nonlinear circuits containing transistors. As a generalization of P0-matrices which are well known in circuit theory and matrix theory, Ω-matrices have many interesting properties. However, no systematic way of constructing Ω-matrices is known so far. This may be because the mathematical structure of Ω-matrices is rather complicated. In this report, we give two simple methods for constructing Ω-matrices that are not P0-matrices. In the first method, all entries in the first row are set to negative values, all entries in the first column and the diagonal line below the first row are set to positive values, and all other entries are set to zero. Here, we should note that only the sign is important for each entry and its absolute value is arbitrary. In the second method, we first construct a matrix by the first method under the condition that the absolute value of each diagonal entry is sufficiently small. Then, by computing the inverse of the matrix, we can obtain an Ω-matrix. The first method generates sparse Ω-matrices, while the second one generates dense Ω-matrices.

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  • A-2-18 ON GRAPHS WITH MAXIMUM OR LOCALLY MAXIMUM GLOBAL CLUSTERING COEFFICIENT

    Teraji Tetsuro, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2013   45 - 45   2013.3

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  • A-2-20 BOUNDEDNESS OF MODIFIED MULTIPLICATIVE UPDATES FOR NMF

    Katayama Jiro, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2013   47 - 47   2013.3

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  • Proof of an inequality related to the Omega-matrix

    NISHI Tetsuo, OISHI Shin'ichi, TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   112 ( 205 )   65 - 70   2012.9

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    This paper gives a complement to the proof of our previous papers, which discussed about some properties of the solution curves of a nonlinear equation obtained from F(x)+Ax=b by deleting the first equation. The theorem is obtained under the assumption that A is an Ω-matrix. By showing rigorously the proof of the previous papers, we confirm that the solution curves possess neither maximal point nor inflection point with respect to the variable x_1.

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  • Proof of an inequality related to the Omega-matrix

    NISHI Tetsuo, OISHI Shin'ich, TAKAHASHI Norikazu

    IEICE technical report. Circuits and systems   112 ( 204 )   65 - 70   2012.9

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    This paper gives a complement to the proof of our previous papers,which discussed about some properties of the solution curves of a nonlinear equation obtained from F(χ) + Aχ = b by deleting the first equation. The theorem is obtained under the assumption that A is an Ω-matrix. By showing rigorously the proof of the previous papers,we confirthat the solution curves possess neither maximal point nor inflection point with respect to the variable χ_<1>.

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  • Some properties of extremal points of solution curves for a class of nonlinear equations

    NISHI Tetsuo, OISHI Shin'ichi, TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   112 ( 117 )   79 - 84   2012.6

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    This paper gives an important theorem on a solution curve of a class of nonlinear equations consisting of n variables and (n - 1) equations, which is obtained from a typical nonlinear equation F(x) + Ax = b by deleting the first equation. The theorem is obtained under the assumption that A is an Ω-matrix, which is a generalization of the P-matrix. Prom this theorem and the previous results we can derive some very important properties on a solution curve. That is, the solution curves consist of only two types of curves.

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  • Global Convergence of a Modified Multiplicative Update Algorithm for Convex Quadratic Programming Problems with Nonnegativity Constraints

    KATAYAMA Jiro, TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   112 ( 117 )   69 - 73   2012.6

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    We consider problems of minimizing a convex quadratic function under nonnegativity constraints. Sha et al. proposed a multiplicative update rule for this problem based on the idea of multiplicative updates for nonnegative matrix factorization. Their update formula has three advantages: 1) nonnegativity of solutions is automatically satisfied, 2) no parameter tuning is needed, and 3) implementation is easy because of simple update formula. However, the global convergence proof given by Sha et al. contains an error. In this paper, we propose a modified version of the multiplicative update and prove its global convergence. We also evaluate through numerical experiments how this modification affects the computation time and the number of iterations.

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  • A-2-23 ON MAXIMALITY OF ALGEBRAIC CONNECTIVITY OF GRAPHS OBTAINED BY ADDING EDGES TO STAR GRAPHS

    Ogiwara Kohnosuke, Fukami Tatsuya, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2012   68 - 68   2012.3

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  • D-20-5 MODIFIED MULTIPLICATIVE UPDATE ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING PROBLEMS WITH NONNEGATIVE CONSTRAINTS

    Katayama Jiro, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2012 ( 2 )   218 - 218   2012.3

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  • On the Rank of a Jacobian Matrix of a Class of Nonlinear Equations

    NISHI Tetsuo, OISHI Shin'ichi, TAKAHASHI Norikazu

    IEICE Tech. Rept   111 ( 486 )   115 - 120   2012.3

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    This paper shows a theorem on the rank of a Jacobian matrix of a class of nonlinear equations consisting of n variables and (n-1) equations and gives its proof. The theorem depends heavily on the properties of both the Ω-matrix and the irreducible matrix.

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  • On the Rank of a Jacobian Matrix of a Class of Nonlinear Equations

    NISHI Tetsuo, OISHI Shin'ichi, TAKAHASHI Norikazu

    IEICE technical report. Communication systems   111 ( 467 )   115 - 120   2012.3

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    This paper shows a theorem on the rank of a Jacobian matrix of a class of nonlinear equations consisting of n variables and (n-1) equations and gives its proof. The theorem depends heavily on the properties of both the Ω-matrix and the irreducible matrix.

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  • On the Rank of a Jacobian Matrix of a Class of Nonlinear Equations

    NISHI Tetsuo, OISHI Shin'ichi, TAKAHASHI Norikazu

    IEICE technical report. Circuits and systems   111 ( 465 )   115 - 120   2012.3

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    This paper shows a theorem on the rank of a Jacobian matrix of a class of nonlinear equations consisting of n variables and (n-1) equations and gives its proof. The theorem depends heavily on the properties of both the Ω-matrix and the irreducible matrix.

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  • On Graphs with Maximum Clustering Coefficient in 2-Switch Neighborhood

    FUKAMI Tatsuya, TAKAHASHI Norikazu

    IEICE technical report. Circuits and systems   111 ( 377 )   13 - 18   2012.1

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    Given a simple undirected connected graph, let us consider the problem to find a graph such that it has the same degree sequence as the given graph, and its the clustering coefficient is the highest among all graphs having the same degree sequence as the given graph. An approach to this problem is to perform local search, that is, to repeat the procedure to find a graph with a higher clustering coefficient among neighbors of the current graph. In this report, we consider a local search based on 2-switch and give some classes of graphs of which the clustering coefficient cannot be increased by this local search.

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  • A Modified Multiplicative Update Algorithm for Nonnegative Matrix Factorization and its Global Convergence : The Case of Divergence Minimization

    HIBI Ryota, TAKAHASHI Norikazu

    IEICE technical report. Circuits and systems   111 ( 377 )   1 - 6   2012.1

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    Nonnegative matrix factorization(NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm proposed by Lee and Seung is widely used as an efficient technique for NMF, it has a serious drawback that the global convergence of the algorithm has not been guaranteed. Recently, the authors proposed a modified multiplicative update algorithm for NMF in which the approximation error is measured by the Euclidean distance between matrices, and proved its global convergence. In this report, we propose a modified multiplicative update algorithm for NMF in which the approximation error is measured by a divergence, and prove its global convergence. We also show that the proposed algorithm always stops within a finite number of iterations if an appropriate stopping criterion is introduced.

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  • A Modified Multiplicative Update Algorithm for Nonnegative Matrix Factorization and its Global Convergence : The Case of Euclidean Distance Minimization

    HIBI Ryota, TAKAHASHI Norikazu

    IEICE technical report   111 ( 106 )   41 - 46   2011.6

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    Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient technique for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this report, we consider NMF in which the approximation error is measured by the Euclidean distance between matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.

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  • Estimation of location parameters using SIFT in image super-resolution

    KIYOTA Yoshitaka, OKUMURA Daisuke, KAWAKITA Masanori, TAKAHASHI Norikazu, TAKEUCHI Jun'ichi

    IEICE technical report   110 ( 457 )   129 - 134   2011.2

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    We propose a computationally efficient method to estimate the location parameters in Bayesian super-resolution (BSR). BSR is one of super-resolution to recover a high-resolution image when several low-resolution images are given. Tipping & Bishop and Pickup et al. proposed BSR-type algorithms. In their BSR algorithms, estimation of location parameters is indispensable and requires much computational cost and memory. Thus, their methods can be applied to only images of small size. To overcome this difficulty, we propose a method estimating the location parameters based on SIFT. Our proposal requires less computational cost and memory. To illustrate its performance, we use a BSR code by Pickup et al. As a result, we succeeded in estimating the location parameters with sufficient accuracy for images having certain properties. In such cases, BSR can be applied to images of relatively large size.

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  • AS-1-1 CONTROLLING THE CLUSTERING COEFFICIENT BASED ON DEGREE PRESERVING TWO-EDGE REWIRING

    Fukami Tatsuya, Takahashi Norikazu

    Proceedings of the IEICE General Conference   2011   "S - 1"-"S-2"   2011.2

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  • Undirected Graphs Maximizing the Second Smallest Eigenvalue of the Graph Laplacian : Case where the Average Degree is Less than or Equal to 2

    OGIWARA Kohnosuke, TAKAHASHI Norikazu

    IEICE technical report   110 ( 389 )   75 - 79   2011.1

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    We consider the problem of finding undirected graphs maximizing the second smallest eigenvalue of the graph Laplacian. The second smallest eigenvalue of the graph Laplacian is an important criterion which determines the speed of convergence of a consensus algorithm for networked multi-agent systems. Let n and m denote the numbers of nodes and edges, respectively. We prove in this report that 1) the cycle graph maximizes the second smallest eigenvalue when n = m and n ≦ 6, 2) a graph obtained by adding an edge to the star graph maximizes the second smallest eigenvalue when n = m and n ≧ 6, and 3) the cycle graph locally maximizes the second smallest eigenvalue for any n ≧ 3.

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  • A Study on Global and Local Maxima of the Clustering Coeffecient

    KOIZUKA Saki, TAKAHASHI Norikazu

    IEICE technical report   110 ( 165 )   49 - 54   2010.7

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    The clustering coefficient is one of the most important indices characterizing complex networks. It is often said that many networks in real world have high clustering coefficients. However, properties of the clustering coefficient have not been discussed much in the literature. This report considers some fundamental problems about the clustering coefficient such as finding the maximum value of the clustering coefficient when the numbers of vertices and edges are fixed and characterizing the structure of the graph that maximizes the clustering coefficient.

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  • Experimental Evaluation of a Two-Phase Sequential Partial Optimization Algorithm for Convex Quadratic Programming Problems

    KOBAYASHI Yuta, TAKAHASHI Norikazu

    IEICE technical report   109 ( 269 )   85 - 90   2009.11

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    A convex quadratic programming (QP) problem is an optimization problem in which a convex quadratic function is minimized subject to some linear constraints. QP problems play important roles in many fields. Recently, the authors have proposed a two-phase sequential partial optimization algorithm for solving general convex QP problems, which is based on the decomposition method for the training of support vector machines. In this report, we describe the algorithm in detail and present experimental results to evaluate its performance.

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  • On the Global Convergence of a Decomposition Method for General Convex Quadratic Programming Problems

    KOBAYASHI Yuta, TAKAHASHI Norikazu

    IEICE technical report   108 ( 388 )   159 - 163   2009.1

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    A convex quadratic programming (QP) problem, which plays important roles in many fields, is an optimization problem to minimize a convex quadratic function subject to some linear constrains. Recently, the authors have developed a new algorithm for solving general convex QP problems, which is based on the decomposition method for the training of support vector machines, and confirmed its effectiveness through experiments. In this report, we analyze theoretically the global convergence property of the algorithm.

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  • A-2-18 PROPOSAL OF A DECOMPOSITION METHOD FOR GENERAL CONVEX QUADRATIC PROGRAMMING PROBLEMS

    Takahashi Norikazu, Kobayashi Yuta, Chen Bo

    Proceedings of the IEICE General Conference   2008   57 - 57   2008.3

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  • On Convergence of State Trajectories of Piecewise-Linear Recurrent Neural Networks Generating Periodic Sequence of Binary Vectors

    MINETOMA Yasuhiro, TAKAHASHI Norikazu

    IEICE technical report   107 ( 349 )   23 - 28   2007.11

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    Recently Takahashi et al. analyzed the behavior of recurrent neural networks with the piecewise-linear output characteristic, and derived a sufficient condition for the network to generate a prescribed periodic sequence of binary vectors such that every two consecutive vectors differ in exactly one component. If a recurrent neural network satisfies this sufficient condition, it is guaranteed that any state trajectory of the network passes through the periodic sequence of regions corresponding to the periodic sequence of binary vectors. However, the asymptotic behavior of the state trajectories has not been clarified yet. In this report, we study the convergence property of state trajectories of a recurrent neural network which satisfies the above-mentioned sufficient condition, and derive a criterion for state trajectories to converge a unique limit cycle. We also make clear the convergence property of the state trajectories for some concrete examples, by checking whether the criterion is satisfied or not.

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  • On Global Convergence of Decomposition Methods for Support Vector Regression

    GUO Jun, TAKAHASHI Norikazu

    IEICE technical report   107 ( 349 )   7 - 12   2007.11

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    To solve the large size quadratic programming (QP) problems arising in support vector regression (SVR) efficiently, decomposition methods are usually used. In a decomposition method, a large QP problem is decomposed into a series of smaller QP subproblems, which can be solved much faster than the original one. In this report, we consider the global convergence of decomposition methods for SVR. We will show the decomposition methods for the convex programming problem formulated by Flake and Lawrence always stop within a finite number of iterations.

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  • Support Vector Machine and its Efficient Learning Algorithms

    TAKAHASHI Norikazu

    IPSJ SIG Notes   2007 ( 96 )   49 - 54   2007.9

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    Support vector machine (SVM) has been attracting considerable attention in the field of pattern recognition, machine learning, and so on. The purpose of this report is to review fundamental principles of the SVM and the decomposition method which is widely used for the training of SVMs. In the first part, some key ideas characterizing SVMs such as margin. maximization, soft margin, and kernel trick are explained. In the second part, the basic idea behind the decomposition method, some representative algorithms, and recent results on its global convergence are introduced.

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    Other Link: http://id.nii.ac.jp/1001/00041060/

  • A stability condition for 2-dimensional Discrete-time Binary Cellular Neural Networks

    OGURA Tomotaka, HARA Hajime, ASANO Toshio, NISHI Tetsuo, TAKAHASHI Norikazu

    IEICE technical report   107 ( 86 )   7 - 11   2007.6

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    We give a stability condition for a two-dimensional discrete-time binary cellular neural networks with an A-template having a simple type of symmetric connection characterized by two independent parameters α and 1β. The results are extension of our previous one-dimensional cases [10], [11].

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  • On Variable Selection in Decomposition Methods for Support Vector Machines : Proposal and Experimental Evaluation of a Novel Variable Selection based on Conjugate Gradient Method

    KAWAZOE Yusuke, KURANOSHITA Masashi, TAKAHASHI Norikazu, TAKEUCHI Jun-ichi

    IEICE technical report   106 ( 588 )   127 - 132   2007.3

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    Learning of a support vector machine (SVM) is formulated as a quadratic programming (QP) problem. Decomposition methods such as sequential minimal optimization algorithm and SVM^<light> are efficient iterative techniques for solving QP problems arising in SVMs. In each step, the decomposition method chooses a small number of variables and then solves the QP problem with respect to those selected variables. In this report, we propose a novel variable selection method based on conjugate gradient method and evaluate its effectiveness by using several benchmark data on both pattern classification and regression problems.

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  • A-2-38 A STUDY ON PERIODIC SEQUENCES OF BINARY PATTERNS REALIZED BY PIECEWISE-LINEAR RECURRENT NEURAL NETWORKS

    Minetoma Yasuhiro, Takahashi Norikazu

    Proceedings of the IEICE General Conference   85 - 85   2007

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  • A-2-6 CONVERGENCE OF STATE TRAJECTORIES OF PIECEWISE-LINEAR RECURRENT NEURAL NETWORKS GENERATING PERIODIC SEQUENCES OF BINARY PATTERNS : TWO NEURON CASE

    Minetoma Yasuhiro, Takahashi Norikazu

    Proceedings of the Society Conference of IEICE   28 - 28   2007

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  • A-2-8 A CONVERGENCE CONDITION FOR DISCRETE-TIME BINARY NEURAL NETWORKS

    Takahashi Norikazu

    Proceedings of the Society Conference of IEICE   2006   39 - 39   2006.9

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  • A Sufficient Condition for 1-D CNNs with Antisymmetric Templates to Perform Connected Component Detection

    ISHITOBI Ken, TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report   106 ( 30 )   15 - 20   2006.5

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    We consider conditions for one-dimensional cellular neural networks (1-D CNNs) with the antisymmetric template A=[s,p,-s] to perform connected component detection (CCD). Given a 1-D black-and-white image, CCD is the task to obtain the output image satisfying 1) the number of black pixels is equal to the number of blocks of consecutive black pixels in the input image, 2) the right-most pixel is black unless all pixels are white, 3) all black pixels are isolated, and 4) there exists exactly one white pixel between two neiboring black pixels. Although it was shown experimentally by Matsumoto et al. that 1-D CNNs with the template A=[1,2,-1] can perform CCD, no theoretical proof has not been known so far. In this report, we analyze the dynamical behavior of 1-D CNNs with the antisymmetric template and give a sufficient condition for such CNNs to perform CCD.

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  • Analysis of Convergence Property of an SMO Algorithm for Support Vector Regression

    GUO Jun, TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report   106 ( 30 )   9 - 14   2006.5

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    Sequential minimal optimization (SMO) algorithms for support vector regression have recently been proposed. However, the convergence of these algorithms has not been proved so far. In this report, we consider a general SMO algorithm and give a rigorous proof that it always satisfies the optimality condition within a finite number of iterations.

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  • Design of Piecewise-Linear Neural Networks Generating Desired Periodic Sequences of Binary Vectors

    TAKAHASHI Norikazu, YAMAKAWA Tsuyoshi, NISHI Tetsuo

    IEICE technical report   105 ( 503 )   43 - 48   2006.1

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    How to design continuous-time neural networks generating prescribed sequences of binary vectors is studied in this report. It is assumed that state-output characteristic of each neuron is expressed by a piecewise linear function and that every two consecutive vectors in the sequence differ in exactly one component. We first analyze the state trajectories of such networks and derive a sufficient condition for the network to generate prescribed sequence of binary vectors. Since this sufficient condition is expressed in the form of linear inequalities, the network design can be formulated as an optimization problem having the sufficient condition as constraints. We will propose two design methods based on this approach : one is to minimize the sum of square of parameter values and the other is to maximize the robustness against parameter variations. Since the former and the latter are formulated as a quadratic programming problem and a linear programming problem, respectively, we can easily find parameter values by applying one of existing numerical solvers.

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  • A-2-1 Reducing the Number of Non-zero Coefficients in the Decision Function of an SVM

    Guo Jun, Takahashi Norikazu, Nishi Tetsuo

    Proceedings of the IEICE General Conference   2005   40 - 40   2005.3

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  • A-1-37 A STUDY ON COMPLETE STABILITY OF THREE-CELL CNNS

    Takahashi Norikazu, Nishi Tetsuo

    Proceedings of the IEICE General Conference   2005   37 - 37   2005.3

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  • Convergence Analysis of Decomposition Methods for Support Vector Machines

    TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report. Neurocomputing   103 ( 734 )   169 - 174   2004.3

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    Convergence property of decomposition methods for support vector machine (SVM) learning is studied. Since learning of an SVM leads to a quadratic programming (QP) problem, it is very important to solve such QP problems efficiently. A decomposition method tries to find an optimum solution of such a QP problem by updating the values of variables iteratively. In each step, a small number of variables are selected based on some criterion and a QP problem with respect to the selected variables is solved. Decomposition methods are known to be useful in particular for large training samples because large matrix computations are not required. However, convergence properties of decomposition methods have not been fully understood so far. In this report, it is proven that a sequence of values obtained by any decomposition method converges to an optimum solution under a mild condition on the variable selection method.

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  • A-2-14 An Efficient Decomposition Learning Method of Support Vector Machinens for Nonlinear Regression

    Kuranoshita Masashi, Takahashi Norikazu, Nishi Tetsuo

    Proceedings of the IEICE General Conference   2004   57 - 57   2004.3

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  • An Application of Fuzzy Support Vector Machines to Nonlinear Regression Problems

    KURANOSHITA Masashi, TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report. Nonlinear problems   103 ( 464 )   81 - 86   2003.11

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    The problem to determine the functional relationship between the input variable and the output variable from given some pairs of the input value and the corresponding output value, which in general contains noise, is called the regression problem. In this report, we apply Fuzzy Support Vector Machines (FSVMs) to the regression problem. The FSVM is an extension of the SVM, which draws considerable attentions in the field of pattern recognition. Since a FSVM deals with each training sample according to the weight or the degree of importance of the sample, it can carry out more flexible pattern classifications than the original SVM. In this report, we first describe how a regression problem is solved by a SVM. Secondly we formulate the method of solving the problem by means of a FSVM and propose a way to determine the weight for each sample. Finally we show via computer simulations that FSVMs have a potential to improve the robustness.

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  • A STUDY ON THE CONVERGENCE PROPERTY OF PLANER DYNAMICAL SYSTEMS RELATED TO CELLULAR NEURAL NETWORKS

    Takahashi Norikazu, Nishi Tetsuo

    Proceedings of the IEICE General Conference   2003   52 - 52   2003.3

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  • A Method for Constrained Optimization Problems by Using SPICE Program

    GUO Jun, NISHI Tetsuo, TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   102 ( 431 )   13 - 18   2002.11

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    Analog Hopfield neural networks (HNNs) have so far been used to solve many kinds of optimization problems,in particular, combinatorial problems such as a TSP. When we solve a minimization problem with equality constraints by using HNNs, however,the constraints are satisfied only approximately. We propose a circuit which rigorously realizes the equality constraints and whose energy function corresponds to the objective function. The constraints may be linear or nonlinear. We use the SPICE program. The proposed method can be applied to several kinds of optimization problems and the results are very satisfied.

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  • An Improvement of the Design Method of Cellular Neural Networks based on Generalized Eigenvalue Problem

    BISE Ryoma, TAKAHASHI Norikazu, NISHI Tetsuo

    Technical report of IEICE. CST   102 ( 428 )   1 - 6   2002.11

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    Recently a design method of cellular neural networks (CNNs) for associative memories based upon generalized eigenvalue minimization problems (GEVMPs) has been proposed. This method is one of the most effective CNN design methods since, by using this method, not only that every prototype vector is stored as a memory vector but also that the basin of attraction of each prototype vector is maximized in a certain sense. In this paper, a new design method of CNNs for associative memories which is based on the above GEVMP-based method will be presented. We first give some analytical results related to the basin of attraction of a memory vector. We then derive the design method by combining those analytical results and the GEVMP-based method. We finally show efficiency of the proposed method by computer simulations.

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  • Necessary and suficient condition for 2-cell cellular neural networks with space-invariant connections to be globally stable

    TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report. Circuits and systems   101 ( 631 )   35 - 42   2002.1

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    A Cellular Neural Network (abbr.CNN) is said to be globally stable if its state converges to some equilibrium point for any initial condition. In this manuscript, by analyzing the phase portrait of certain CNNs consisting of two cells in detail, we will give a new sufficient condition for those CNNs to be globally stable. Moreover, combining the results in this manuscript with the conventional ones, we will also give a necessary and sufficient condition for CNNs consisting of two cells to be globally stable under the assumptions that i) connections between cells are space-invariant, ii) self-feedback coefficients are greater than 1,and iii) there is no external input.

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  • Generalization of Two Complete Stability Conditions for DCNN's

    Takahashi Norikazu, Nishi Tetuo

    Proceedings of the IEICE General Conference   2001   15 - 15   2001.3

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  • On the extension of Tadeusiewicz's sufficient condition for DC operating points to be asymptotically stable in transistor circuits

    OGATA Masato, TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report. Nonlinear problems   100 ( 608 )   17 - 23   2001.1

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    In this paper we discuss asymptotic stability of DC operating points in transistor circuits. The stability of DC operating points is examined for any dynamic circuits derived from the resistive circuit by augmenting parasitic reactances. We derive a sufficient condition for the Lyapunov equation of any dynamic circuits obtained by adding capacitors to have a positive diagonal solution. The extension of Tadeusiewicz's sufficient condition for asymptotically stable DC operating points is also considered.

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  • Complete Stability Analysis of Cellular Neural Networks Consisting of Two Cells

    TAKAHASHI Norikazu, NISHI Tetsuo

    IEICE technical report. Nonlinear problems   100 ( 608 )   9 - 16   2001.1

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    A Cellular Neural Network(CNN)is a high dimensional nonlinear dynamical system in which various nonlinear phenomena including chaos, limit cycle, pattern formation take place. In many applications such as image processing, it is important to ensure that a CNN converges to an equilibrium state for any initial state and any threshold value, that is, a CNN is completely stable. Therefore, the complete stability is one of the most fundamental research topics in the field of CNN dynamics. Although Civalleri et al.analyzed the global dynamics of CNN's consisting of two cells, they treated only the case of zero threshold. Moreover, their results contain some errors. Thus, in the present manuscript, we will make clear the condition under which a two-cell CNN is completely stable or unstable by investigating the phase portrait in detail.

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  • A Design Method of Cellular Neural Networks with Symmetric Connections for Associative Memories

    BISE Ryoma, TAKAHASHI Norikazu, NISHI Tetsuo

    Technical report of IEICE. CST   100 ( 418 )   17 - 22   2000.11

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    This report deals with the problem of designing cellular neural networks (CNNs) for associative memories. Concerning the problem, a design method of sparsely connected neural networks by means of the singular value decomposition has been proposed, and we can design CNNs by using this method. However this method has a problem that the complete stability of a designed CNN is not guarateed because the CNN has non-symmetric connections in general. In this report, we give a new design method of CNNs which guarantees the symmetry of connections. Any CNN designed by our method is completely stable, because it has been proved that a CNN with symmetric connections is completely stable.

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  • Generalization of Complete Stability Conditions of Neural Networks with Piecewise Linear Output Function

    TAKAHASHI Norikazu

    Technical report of IEICE. VLD   100 ( 121 )   69 - 74   2000.6

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    A recurrent neural network is said to be completely stable if its state trajectory converges to an equilibrium point for any initial condition. The author recently derived a sufficient condition for recurrent neural networks with the piecewise linear output function to be completely stable. In this report, a new complete stability condition which is a generalization of the above mentioned sufficient condition is given. A convergence theorem of the Gauss-Seidel method, which is a well-known iterative technique for solving linear algebraic equations, plays an important role while most of the conventional stability criteria were obtained by constructing Lyapunov functions.

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  • A Study on Asymptotically Stable DC Operating Points of Nonlinear Resistive Circuits

    OGATA Masato, TAKAHASHI Norikazu, NISHI Tetsuo

    Technical report of IEICE. VLD   100 ( 121 )   75 - 81   2000.6

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    Practically speaking, it is well known that in a nonlinear resistive circuit with multiple operating points some of them are unstable. However, the problem of specifying the stability of each operating point is still not completely solved. The stability of operating points is often defined in terms of the stability of equilibrium points. Tadeusiewicz derived a sufficient condition for asymptotically stable operating points of nonlinear resistive circuits with dependent current sources on the basis of parallel capacitors. In this paper, we discuss asymptotically stable operating point of nonlinear resistive circuits with dependent current and voltage sources. Our definition about stability of operating points treats a broader class of dynamic circuit than one of Tadeusiewicz. A sufficient condition for identifying asymptotically stable operating points is derived.

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  • Recurrent Networks with Hidden Units Learned by Hebb's Rule and Back-Propagation Method for Auto-Associative Memory

    TSUZURUGI Jun, TAKAHASI Norikazu

    IEICE technical report. Neurocomputing   99 ( 685 )   169 - 176   2000.3

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    It is well known that many spurious memories arise in an auto-associative memory or a multi-layer network which uses back-propagation method. In this paper, we apply recurrent networks with hidden units to auto-associative memory, and propose a learning method which seldom generates spurious memories. The proposed learning method uses both Hebb's rule and back-propagation method. It is thought that the combination of these two methods can effectively delete the candidates for spurious memories, which would occur if we used only one method. Simulation results show that the proposed method actually seldom generates spurious memories.

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  • On the Stability of Neural Networks with Piecewise Linear Output Function

    Takahashi Norikazu

    Proceedings of the IEICE General Conference   2000   64 - 64   2000.3

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  • On the Complete Stability of Cellular Neural Networks with Delay

    TAKAHASHI Norikazu

    IEICE technical report. Nonlinear problems   98 ( 583 )   31 - 38   1999.2

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    This paper gives a new sufficient condition for Cellular Neural Networks with Delay (DC-NN's) to be completely stable. A DCNN is said to be completely stable if and only if its trajectory converges to and equilibrium point for any initial condition. Most of the conventional stability criteria were obtained by constructing Lyapunov functions. On the other hand, a convergence theorem of the Gauss-Seidel method, which is a well-known iterative technique for solving linear algebraic equations, plays an important role in this paper.

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  • A New Associative Memory Algorithm with Multiple Hopfiled Neural Networks

    TSUZURUGI Jun, TAKAHASHI Norikazu

    IEICE technical report. Neurocomputing   98 ( 526 )   1 - 7   1999.1

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    Generalized Hebbian rule which is sometimes referred to as the outer product method is the most well-known learning algorithm for associative memory with Hopfield neural networks. The algorithm of the generalized Hebbian rule is very simple, but there is a serious problem that if we store many patterns with this rule then a number of spurious memories arise in general. In this paper, we propose a new learning and recalling algorithm which never generates spurious memories. The algorithm is summarized as follows: 1)A given set of memory patterns is devided into some groups, and for each group, we store the memory patterns to a Hopfield neural network by using the generalized Hebbian rule. 2)We impose a given input pattern on every network as the initial state, and find the final state of each network. 3)If some of the networks converged to a spurious memory, these networks and the corresponding memory patterns are removed. 4)We repeat 1) to 3) until only one network is remained. The final state of the remaining Hopfield neural network is regarded as the output of our new algorithm.

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  • My Opinion about the Difference in Campus Life between Japan and USA

    TAKAHASHI Norikazu

    The Journal of the Institute of Electronics,Information and Communication Engineers   81 ( 8 )   866 - 868   1998.8

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  • A Study on the Global Stability of Neural Networks with the Piecewise Linear Functions

    NISHI Tetsuo, TAKAHASHI Norikazu

    IEICE technical report. Circuits and systems   96 ( 125 )   1 - 8   1996.6

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    Global stability is one of the most important property of the neural network for its various applications. As is well known, neural networks with the symmetric connections are globally stable. On the other hand, it is very difficult to discuss the global stability of neural networks with the nonsymmetric connections. This paper studies on the global stability of neural networks with two neurons. We assume that the output function of each neuron is piecewise-linear, and that the connection matrix can be diagonalized. Characterizing the global stability by eigenvalues and eigenvectors of the connection matrix, we give new sufficient conditions for the neural networks with two neurons to be globally stable.

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  • On the Number of Equilibrium Points and Basin of Attraction of a Kind of Neural Network

    TAKAHASHI Norikazu, NISHI Tetsuo

    Proceedings of the IEICE General Conference   1995   88 - 88   1995.3

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  • Realization of Equilibrium Points by Means of a Completely Symmetrical Nonlinear Circuit

    TAKAHASHI Norikazu, NISHI Tetsuo

    Memoirs of the Faculty of Engineering, Kyushu University   54 ( 2 )   141 - 160   1994.6

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  • On the set of equilibrium points of one-dimensional neural networks with tapered connecting coefficients

    Takahashi Norikazu, Nishi Tetsuo

    IEICE technical report. Circuits and systems   93 ( 432 )   83 - 90   1994.1

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    In general,it is very difficult to synthesize a mutually coupled neural network which has only a desired set of equilibrium points. This paper studies on the synthesis of a set of equilibrium points of a mutually coupled neural network of which the neurons are arranged on a ring and have their connections with k(【less tha n or equal】4)forward neurons only.We first investigate the charact eristics of a set of equilibrium points of this network,especially the number of equilibrium points.Next we give the necessary and sufficient condition for a set of vectors to be an exact set of equilibrium points.

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  • On the Equilibrium Points of Mutually Coupled Circuits with Symmetrical Structure

    1992 ( 43 )   125 - 130   1992.5

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Presentations

  • Deep learning of OpenStreetMap images labeled using road traffic accident data

    Kaito Arase, Zhijian Wu, Tsuyoshi Migita, Norikazu Takahashi

    2022 IEEE Region 10 Conference  2022.11.3 

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  • A faster algorithm to search for generalized Moore graphs

    Taku Hirayama, Tsuyoshi Migita, Norikazu Takahashi

    2022 IEEE Region 10 Conference  2022.11.1 

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  • 交通事故データに基づき地図画像を学習させたCNNの判断根拠の可視化

    荒瀬快斗, 呉志堅, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2022.6.9 

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    Event date: 2022.6.9 - 2022.6.10

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  • 一般化ムーアグラフ探索アルゴリズムの高速化

    平山拓, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2022.6.9 

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    Event date: 2022.6.9 - 2022.6.10

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  • Uncalibrated photometric stereo using superquadrics with texture estimatio

    Tsuyoshi Migita, Ayane Okada, Norikazu Takahashi

    The 28th International Workshop on Frontiers of Computer Vision  2022.2.21 

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    Event date: 2022.2.21 - 2022.2.22

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  • Distributed HALS algorithm for NMF based on simple average consensus algorithm

    Keiju Hayashi, Tsuyoshi Migita, Norikazu Takahashi

    2021 IEEE International Conference on Progress in Informatics and Computing  2021.12.18 

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    Event date: 2021.12.17 - 2021.12.19

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  • An algorithm for randomized nonnegative matrix factorization and its global convergence

    Takao Masuda, Tsuyoshi Migita, Norikazu Takahashi

    2021 IEEE Symposium Series on Computational Intelligence  2021.12.7 

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    Event date: 2021.12.5 - 2021.12.7

    Language:English   Presentation type:Oral presentation (general)  

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  • Finding a generalized Moore graph using randomized depth-first search

    Yoshiki Satotani, Norikazu Takahashi

    2021 Graph Golf Workshop,  2021.11.24 

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    Event date: 2021.11.24

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  • べき乗法と平均合意に基づく分散的主成分分析アルゴリズムの性能評価

    大浦夢月, 右田剛史, 高橋規一

    2021年度(第72回)電気・情報関連学会中国支部連合大会  2021.10.23 

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    Event date: 2021.10.23

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • 交通事故危険箇所予測のための地図画像の深層学習

    呉志堅, 右田剛史, 高橋規一

    2021年度(第72回)電気・情報関連学会中国支部連合大会  2021.10.23 

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    Event date: 2021.10.23

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  • マルチニューラルネットワークの分散学習におけるパラメータ値送受信法の提案

    萱谷竜也, 右田剛史, 高橋規一

    2021年度(第72回)電気・情報関連学会中国支部連合大会  2021.10.23 

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    Event date: 2021.10.23

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • NMFのための分散HALS法における平均合意アルゴリズムの単純化

    林京寿, 右田剛史, 高橋規一

    電子情報通信学会情報論的学習理論と機械学習研究会  2021.6.28 

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    Event date: 2021.6.28 - 2021.6.30

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  • ランダム化NMFにおける最適化問題の修正とHALS法に基づく解法の提案

    舛田昂生, 右田剛史, 高橋規一

    電子情報通信学会情報論的学習理論と機械学習研究会  2021.6.28 

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    Event date: 2021.6.28 - 2021.6.30

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  • マルチニューラルネットワークの新たな分散学習アルゴリズムの提案

    原田和明, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2021.3.15 

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    Event date: 2021.3.15 - 2021.3.16

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  • 遺伝的アルゴリズムを用いたグラフの構造最適化

    田尻紘生, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2021.3.15 

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    Event date: 2021.3.15 - 2021.3.16

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  • エッジ画像とグレースケール画像を用いた段階的超解像モデル

    平田大貴, 高橋規一

    2021年電子情報通信学会総合大会  2021.3.9 

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    Event date: 2021.3.9 - 2021.3.12

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  • Uncalibrated photometric stereo using superquadrics with cast shadow

    Takumi Nasu, Tsuyoshi Migita, Norikazu Takahashi

    The 27th International Workshop on Frontiers of Computer Vision  2021.2.23 

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    Event date: 2021.2.22 - 2021.2.23

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  • Distributed algorithm for principal component analysis based on power method and average consensus algorithm

    Norikazu Takahashi, Mutsuki Oura, Tsuyoshi Migita

    2020 International Conference on Progress in Informatics and Computing  2020.12.19 

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    Event date: 2020.12.18 - 2020.12.20

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  • A genetic algorithm for finding regular graphs with minimum average shortest path length

    Reiji Hayashi, Tsuyoshi Migita, Norikazu Takahashi

    2020 IEEE Symposium Series on Computational Intelligence  2020.12.4 

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    Event date: 2020.12.1 - 2020.12.4

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  • 代数的連結度推定のための擬似分散的連続時間アルゴリズムの一般化

    島田捷生, 右田剛史, 高橋規一

    電子情報通信学会システム数理と応用研究会  2020.11.25 

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    Event date: 2020.11.25 - 2020.11.26

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  • 乗法型更新と合意形成に基づく非負値行列因子分解の分散計算アルゴリズム

    道免陽平, 右田剛史, 高橋規一

    電子情報通信学会システム数理と応用研究会  2020.11.25 

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    Event date: 2020.11.25 - 2020.11.26

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  • Element-wise alternating least squares algorithm for nonnegative matrix factorization on one-hot encoded data

    Zhuo Wu, Tsuyoshi Migita, Norikazu Takahashi

    The 27th International Conference on Neural Information Processing  2020.11.20 

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    Event date: 2020.11.18 - 2020.11.22

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  • ワンホット表現データに対する非負値行列因子分解のための要素ごとの交互最小二乗アルゴリズム

    呉濯, 右田剛史, 高橋規一

    2020年度(第71回)電気・情報関連学会中国支部連合大会  2020.10.24 

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  • L1正則化非負値行列因子分解のための新たな階層的交互最小二乗法

    佐野雄大, 右田剛史, 高橋規一

    第19回情報科学技術フォーラム  2020.9.1 

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    Event date: 2020.9.1 - 2020.9.3

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  • クラスタアンサンブルを利用したGNMFに基づくクラスタリングの性能評価

    佐野雄大, 右田剛史, 高橋規一

    2020年度人工知能学会全国大会(第34回)  2020.6.12 

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    Event date: 2020.6.9 - 2020.6.12

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  • 正則グラフの平均頂点間距離最小化のための遺伝アルゴリズム

    林嶺司, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2020.5.15 

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    Event date: 2020.5.15

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  • べき乗法と平均合意に基づく主成分分析の分散アルゴリズムの設計

    大浦夢月, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2020.5.15 

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  • 全結合層階層化CNNにおける判別器併合法

    平田大貴, 高橋規一

    2020年電子情報通信学会総合大会  2020.3.19 

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    Event date: 2020.3.17 - 2020.3.20

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  • GNMFのための修正乗法型更新式とその大域収束性

    佐野雄大, 右田剛史, 高橋規一

    2020年電子情報通信学会総合大会  2020.3.18 

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    Event date: 2020.3.17 - 2020.3.20

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  • 凸2次関数の逐次最小化に基づくSandberg-Willson方程式の分散解法

    武内雅章, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2020.3.9 

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    Event date: 2020.3.9 - 2020.3.10

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  • 射影合意に基づく非負制約付き連立一次方程式の最大誤差最小化アルゴリズム

    川嶌康輔, 右田剛史, 高橋規一

    電子情報通信学会非線形問題研究会  2020.3.9 

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    Event date: 2020.3.9 - 2020.3.10

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  • Uncalibrated photometric stereo using quadric surfaces with two cameras

    Takumi Nasu, Tsuyoshi Migita, Takeshi Shakunaga, Norikazu Takahashi

    The 26th International Workshop on Frontiers of Computer Vision  2020.2.21 

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    Event date: 2020.2.20 - 2020.2.22

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  • An infinity norm-based pseudo-decentralized discrete-time algorithm for computing algebraic connectivity

    Katsuki Shimada, Tsuyoshi Migita, Norikazu Takahashi

    2019 IEEE Symposium Series on Computational Intelligence  2019.12.9 

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    Event date: 2019.12.6 - 2019.12.9

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  • A distributed HALS algorithm for Euclidean distance-based nonnegative matrix factorization

    Yohei Domen, Tsuyoshi Migita, Norikazu Takahashi

    2019 IEEE Symposium Series on Computational Intelligence  2019.12.9 

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    Event date: 2019.12.6 - 2019.12.9

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  • A genetic algorithm for maximizing algebraic connectivity of graphs by adding multiple edges

    Hiroki Tajiri, Tsuyoshi Migita, Norikazu Takahashi

    2019 International Symposium on Nonlinear Theory and Its Applications  2019.12.3 

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    Event date: 2019.12.2 - 2019.12.6

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  • New rules for choosing values of consensus weights in distributed training of neural networks

    Kazuaki Harada, Tsuyoshi Migita, Norikazu Takahashi

    2019 International Symposium on Nonlinear Theory and Its Applications  2019.12.3 

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    Event date: 2019.12.2 - 2019.12.6

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  • Mutual relationship between the neural network model and linear complexity for pseudorandom binary number sequence

    Yuki Taketa, Yuta Kodera, Shogo Tanida, Takuya Kusaka, Yasuyuki Nogami, Norikazu Takahashi, Satoshi Uehara

    The Seventh International Symposium on Computing and Networking Workshops  2019.11.27 

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    Event date: 2019.11.27 - 2019.11.29

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  • A damped Newton algorithm for nonnegative matrix factorization based on alpha-divergence

    Takehiro Sano, Tsuyoshi Migita, Norikazu Takahashi

    2019 6th International Conference on Systems and Informatics  2019.11.3 

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    Event date: 2019.11.2 - 2019.11.4

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  • 合意に基づく分散アルゴリズムと機械学習への応用 Invited

    高橋規一

    電子情報通信学会スマートインフォメディアシステム研究会  2019.12.12 

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  • 光源の異なる画像を用いた楕円体と一葉双曲面のパラメータ推定

    那須巧海, 右田剛史, 尺長健, 高橋規一

    第18回情報科学技術フォーラム  2019.9.5 

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  • 単調方程式のニュートン型解法に基づく新たな非負値行列因子分解アルゴリズム

    佐野雄大, 右田剛史, 高橋規一

    第18回情報科学技術フォーラム  2019.9.5 

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  • マルチエージェントネットワークによる非負値行列因子分解の分散計算

    道免陽平, 右田剛史, 高橋規一

    第18回情報科学技術フォーラム  2019.9.5 

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  • 遺伝アルゴリズムによる代数的連結度最大化

    田尻紘生, 高橋規一

    第18回情報科学技術フォーラム  2019.9.3 

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  • マイコン実装したAES暗号に対するCNNを用いた最終ラウンド鍵の解析

    小杉聡志, 城市翔, 生田健, 日下卓也, 野上保之, 高橋規一

    第18回情報科学技術フォーラム  2019.9.3 

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  • ニューラルネットワークの分散学習における新たな合意重み決定法

    原田和明, 高橋規一

    第18回情報科学技術フォーラム  2019.9.3 

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  • 無限大ノルムを用いて代数的連結度を計算する擬似分散的離散時間アルゴリズム

    島田捷生, 高橋規一

    2019年電子情報通信学会NOLTAソサイエティ大会  2019.6.8 

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  • 畳み込みニューラルネットワークの階層的判別器構築によるパラメータ数の削減

    平田大貴, 高橋規一

    電子情報通信学会2019年総合大会  2019.3.21 

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  • 辺削除時の媒介中心性の高速更新法

    里谷佳紀, 高橋規一

    電子情報通信学会2019年総合大会  2019.3.20 

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  • マイコン実装したAES暗号に対するニューラルネットワークを用いた最終ラウンド鍵の解析

    小杉聡志, 城市翔, 生田健, 日下卓也, 野上保之, 高橋規一

    電子情報通信学会情報セキュリティ研究会  2019.3.7 

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  • A novel NMF algorithm for detecting clusters in directed networks International conference

    Yoshito Usuzaka, Norikazu Takahashi

    2019 Workshop on Computing, Networking and Communications  2019.2.18 

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  • 誤差関数が対数を含む場合の非負値行列因子分解の新たな乗法型更新式導出法

    高祖晶弘, 高橋規一

    電子情報通信学会非線形問題研究会  2019.1.24 

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  • A genetic algorithm-based method for finding approximate solutions to minimum steiner tree problems

    Li-Ping Zhang, Norikazu Takahashi, Zong-Xiao Yang

    2019.1.24 

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  • FPGA上に実装したCurve25519への位数4及び8の有理点を用いたサイドチャネル攻撃に関する考察

    眞田晃宏, 上竹嘉紀, 日下卓也, 野上保之, 高橋規一

    2019年暗号と情報セキュリティシンポジウム  2019.1.24 

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  • Depth-first search algorithms for finding a generalized Moore graph International conference

    Yoshiki Satotani, Norikazu Takahashi

    2018 IEEE Region 10 Conference  2018.10.30 

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  • 代数的連結度計算のための擬似分散的離散時間アルゴリズムの収束性 ~ 代数的連結度が重複する場合の解析 ~

    浦上朋久, 高橋規一

    電子情報通信学会非線形問題研究会  2018.10.19 

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  • A distributed algorithm for solving Sandberg-Willson equations International conference

    Masaaki Takeuchi, Norikazu Takahashi

    2018 International Symposium on Nonlinear Theory and Its Applications  2018.9.4 

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  • Reconstruction of CT images by iterative least squares methods with nonnegative constraint, International conference

    Hiromasa Kohno, Yuichi Tanji, Ken'ichi Fujimoto, Hiroyuki Kitajima, Yo Horikawa, Norikazu Takahashi

    2018 International Symposium on Nonlinear Theory and Its Applications  2018.9.3 

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  • コミュニティ検出のための新たな非負値行列因子分解アルゴリズムの導出と実験的評価

    薄坂誼人, 高橋規一

    電子情報通信学会非線形問題研究会  2018.8.9 

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  • 構造時不変ネットワーク上の射影合意アルゴリズムの収束条件

    川嶌康輔, 高橋規一

    電子情報通信学会非線形問題研究会  2018.8.9 

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  • 非負値拘束を有する反復最小2乗法によるCT画像の再構成

    河野紘正, 丹治裕一, 藤本憲市, 北島博之, 堀川洋, 高橋規一

    電子情報通信学会非線形問題研究会  2018.8.8 

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  • 一般化ムーアグラフの効率的探索法の提案と評価

    里谷佳紀, 高橋規一

    電子情報通信学会非線形問題研究会  2018.6.10 

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  • マルチエージェントネットワークによるSandberg-Willson方程式の分散解法

    武内雅章, 高橋規一

    電子情報通信学会非線形問題研究会  2018.4.27 

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  • 対数を含む誤差関数に基づくNMFの乗法型更新式の新たな統一的導出法

    高祖晶弘, 高橋規一

    電子情報通信学会2018年総合大会  2018.3.21 

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  • 代数的連結度推定のための真に分散的な離散時間アルゴリズムの平衡点解析

    遠藤拳人, 高橋規一

    電子情報通信学会非線形問題研究会  2018.1.26 

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  • 一般化de Bruijnグラフに基づく単純無向正則グラフ構成法

    石井涼也, 高橋規一

    電子情報通信学会非線形問題研究会  2018.1.26 

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  • 有向ネットワークに対するコミュニティ検出のための高速な非負値行列因子分解アルゴリズム

    薄坂誼人, 高橋規一

    2018年電子情報通信学会NOLTAソサイエティ大会  2018 

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  • Analysis of a pseudo-decentralized discrete-time algorithm for estimating algebraic connectivity of multiagent networks International conference

    Tomohisa Urakami, Norikazu Takahashi

    2017 International Symposium on Nonlinear Theory and Its Applications  2017.12.6 

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  • Derivation of multiplicative update rules for nonnegative matrix factorization with regularization terms International conference

    Akihiro Koso, Norikazu Takahashi

    2017 International Symposium on Nonlinear Theory and Its Applications  2017.12.5 

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  • マルチエージェントネットワークの代数的連結度を推定する離散時間アルゴリズムの収束性解析

    浦上朋久, 高橋規一

    平成29年度(第68回)電気・情報関連学会中国支部連合大会  2017.10.21 

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  • 非負値行列因子分解を用いたCT画像の再構成

    河野紘正, 丹治裕一, 藤本憲市, 高橋規一

    電子情報通信学会非線形問題研究会  2017.10.6 

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  • 辺数が頂点数に近い場合の大域クラスター係数最大グラフ

    栗城亮夏, 高橋規一

    電子情報通信学会非線形問題研究会  2017.10.6 

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  • 重み付き無向グラフの媒介中心性の更新式

    難波俊行, 高橋規一

    2017年電子情報通信学会ソサイエティ大会  2017.9.13 

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  • Image reconstruction for computed tomography by nonnegative matrix factorization International conference

    Hiromasa Kohno, Yuichi Tanji, Ken'ichi Fujimoto, Norikazu Takahashi

    2017 Taiwan and Japan Conference on Circuits and Systems  2017.8.22 

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  • Equilibrium point analysis of a decentralized discrete-time system for algebraic connectivity estimation International conference

    Kento Endo, Norikazu Takahashi

    2017 Taiwan and Japan Conference on Circuits and Systems  2017.8.22 

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  • αダイバージェンスに基づく非負値行列因子分解のためのニュートン法型アルゴリズム

    中津智史, 高橋規一

    電子情報通信学会非線形問題研究会  2017.7.13 

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  • マルチエージェントネットワークの代数的連結度推定のための擬似分散的離散時間アルゴリズム

    浦上朋久, 高橋規一

    電子情報通信学会非線形問題研究会  2017.5.11 

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  • 正則化項が導入された非負値行列因子分解のための乗法型更新式の導出

    高祖晶弘, 高橋規一

    電子情報通信学会非線形問題研究会  2017.5.11 

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  • 辺数と頂点数の差が4以下の場合の大域クラスター係数最大グラフ

    栗城亮夏, 高橋規一

    電子情報通信学会2017年総合大会  2017.3.22 

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  • スパースさと滑らかさを調整できる非負値行列因子分解の新しい反復計算法と大域収束性

    木村匠, 高橋規一

    電子情報通信学会信号処理研究会  2017.1.20 

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  • 出現頻度が急変するアイテムを検出するストリームアルゴリズムの性能評価

    木下毅, 高橋規一

    電子情報通信学会信号処理研究会  2017.1.19 

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  • A novel Newton-type algorithm for nonnegative matrix factorization with alpha-divergence International conference

    Satoshi Nakatsu, Norikazu Takahashi

    24th International Conference on Neural Information Processing  2017 

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  • Extensions of a theorem on algebraic connectivity maximizing graphs International conference

    Ryoya Ishii, Norikazu Takahashi

    2016 International Symposium on Nonlinear Theory and its Applications  2016.11.30 

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  • A fast method for finding the edge to be added to minimize betweenness centrality of a specified vertex International conference

    Toshiyuki Namba, Norikazu Takahashi

    2016 International Symposium on Nonlinear Theory and its Applications  2016.11.30 

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  • A new decentralized discrete-time algorithm for estimating algebraic connectivity of multiagent networks International conference

    Kento Endo, Norikazu Takahashi

    2016 IEEE Asia Pacific Conference on Circuits and Systems  2016.10.27 

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  • αダイバージェンスを誤差とする非負値行列因子分解のためのニュートン法に基づく反復計算法の提案

    中津智史, 高橋規一

    平成28年度(第67回)電気・情報関連学会中国支部連合大会  2016.10.22 

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  • 頂点数と辺数の制約下で代数的連結度が最大となる完全多部グラフに関する考察

    石井涼也, 高橋規一

    電子情報通信学会非線形問題研究会  2016.9.15 

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  • 指定頂点の媒介中心性を最小にする辺挿入位置の高速探索法

    難波俊行, 高橋規一

    電子情報通信学会非線形問題研究会  2016.9.15 

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  • マルチエージェントネットワークにおける代数的連結度推定のための新しい分散的離散時間アルゴリズム

    遠藤拳人, 高橋規一

    電子情報通信学会非線形問題研究会  2016.9.15 

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  • Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence International conference

    Norikazu Takahashi, Masato Seki

    2016 European Signal Processing Conference  2016.8.30 

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  • 代数的連結度最大グラフに関する一定理の拡張

    石井涼也, 高橋規一

    電子情報通信学会2016年総合大会  2016.3.17 

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  • 出現頻度が急変するアイテムを検出するストリームアルゴリズム

    木下毅, 高橋規一

    電子情報通信学会2016年総合大会  2016.3.15 

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  • 完全多部グラフの代数的連結度最大性と2-switchに基づく代数的連結度極大グラフ探索法

    藤原拓郎, 高橋規一

    電子情報通信学会高信頼制御通信研究会  2016.1.29 

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  • 一般化誤差関数に基づく非負値行列因子分解に対する乗法型更新式とその大域収束性の解析

    関真慧, 高橋規一

    電子情報通信学会信号処理研究会  2016.1.18 

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  • Global convergence of a modified HALS algorithm for nonnegative matrix factorization International conference

    Takumi Kimura, Norikazu Takahashi

    2015.12.14 

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  • 2-switch近傍に基づく大域クラスター係数極大グラフに関する一考察

    平成27年度(第66回)電気・情報関連学会中国支部連合大会  2015 

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  • 非負値行列因子分解に関連する制約付き最適化問題に対する乗法型更新式の導出とその大域収束性の解析

    電子情報通信学会非線形問題研究会  2015 

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  • マルチエージェントネットワークにおける真に分散的な代数的連結度推定アルゴリズムの提案

    電子情報通信学会非線形問題研究会  2015 

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  • 完全多部グラフの代数的連結度極大性

    電子情報通信学会2015年総合大会  2015 

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  • 非負値行列因子分解のための階層的交互最小二乗法の修正とその大域収束性

    電子情報通信学会2015年総合大会  2015 

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  • 離散時間2値ニューラルネットワークの一収束条件を判定する多項式時間アルゴリズム

    電子情報通信学会2015年総合大会  2015 

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  • 短い平均頂点間距離をもつ正則グラフの生成法

    電子情報通信学会非線形問題研究会  2015 

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  • Complete multipartite graphs maximize algebraic connectivity in the neighborhood based on 2-switch

    2015 International Symposium on Nonlinear Theory and its Applications  2015 

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  • Proposal of a truly decentralized algorithm for estimating algebraic connectivity of multi-agent networks

    2015 International Symposium on Nonlinear Theory and its Applications  2015 

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  • 2次元データの列に対するストリームアルゴリズムの改良

    第38回情報理論とその応用シンポジウム  2015 

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  • 非負値行列因子分解のための階層的交互最小二乗法の大域収束性解析

    第38回情報理論とその応用シンポジウム  2015 

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  • マルチエージェントネットワークの代数的連結度推定アルゴリズムにおける正規化法の拡張

    第58回自動制御連合講演会  2015 

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  • On graphs that locally maximize algebraic connectivity in the space of graphs with the fixed degree sequence

    2014 International Symposium on Nonlinear Theory and its Applications  2014 

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  • 非負値行列因子分解のためのKL, Gamma, Renyiダイバージェンスに基づく新たな更新式の導出

    電子情報通信学会信号処理研究会  2014 

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  • 2-switchに基づく代数的連結度最大グラフ探索法と次数3の正則グラフへの適用

    電子情報通信学会非線形問題研究会  2014 

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  • 同一次数列をもつグラフ族における代数的連結度極大グラフ - 完全2部グラフの場合 -

    電子情報通信学会2014年総合大会  2014 

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  • 離散時間二値ニューラルネットワークの収束条件判定アルゴリズム

    電子情報通信学会2014年総合大会  2014 

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  • 行列の条件数の最大値に関する考察

    電子情報通信学会非線形問題研究会  2014 

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  • 離散時間2値ニューラルネットワークの収束条件に関連するある判定問題のNP完全性

    平成26年度(第65回)電気・情報関連学会中国支部連合大会  2014 

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  • A generalized sufficient condition for global convergence of modified multiplicative updates for NMF

    2014 International Symposium on Nonlinear Theory and its Applications  2014 

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  • New update rules based on Kullback-Leibler, gamma, and Renyi divergences for nonnegative matrix factorization

    2014 International Symposium on Nonlinear Theory and its Applications  2014 

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  • Finding Items Associated with Varied Members in A Pairwise Data Stream

    第16回アルゴリズムと計算に関する韓国-日本共同会議  2013 

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  • 非負値行列因子分解のための修正乗法型更新式の有界性

    電子情報通信学会2013年総合大会  2013 

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  • 大域クラスター係数が最大または極大となるグラフについて

    電子情報通信学会2013年総合大会  2013 

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  • 情報理論によるシングルフレーム超解像の限界性能評価

    電子情報通信学会情報論的学習理論と機械学習研究会  2013 

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  • Boundedness of modified multiplicative updates for nonnegative matrix factorization

    第5回IEEEマルチセンサ適応信号処理のための計算法の進化に関する国際会議  2013 

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  • Ω行列の系統的構成法に関する一考察

    電子情報通信学会非線形問題研究会  2013 

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  • 非負値行列因子分解のための各種乗法型更新式の修正と有界性

    第23回インテリジェント・システム・シンポジウム  2013 

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  • On Graphs that Locally Maximize Global Clustering Coefficient

    2013年非線形理論とその応用に関する国際会議  2013 

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  • 2-Switch近傍において最大クラスター係数をもつグラフについて

    電子情報通信学会回路とシステム研究会  2012 

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  • 単一フレーム超解像の限界について

    第35回情報理論とその応用シンポジウム  2012 

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  • 与えられた頂点数と辺数の下で代数的連結度を最大にするグラフについて

    九州大学組合せ数学セミナー  2012 

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  • A New Continuous-Time Algorithm for Calculating Algebraic Connectivity of Multi-Agent Networks

    2012年非線形理論とその応用に関する国際会議  2012 

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  • A Theorem on a Solution Curve of a Class of Nonlinear Equations

    2012年非線形理論とその応用に関する国際会議  2012 

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  • A Modified Multiplicative Update Algorithm for Convex Quadratic Programming Problems with Nonnegativity Constraints

    2012年非線形理論とその応用に関する国際会議  2012 

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  • マルチエージェントネットワークの代数的連結度計算法の拡張

    平成24年度電気関係学会九州支部連合大会  2012 

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  • 非負制約付き2次計画問題に対する修正乗法型更新アルゴリズム

    平成24年度電気関係学会九州支部連合大会  2012 

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  • Proof of an inequality related to the Omega-matrix

    電子情報通信学会回路とシステム研究会  2012 

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  • Information Theoretic Limit of Single-Frame Super-Resolution

    第3回新しいセキュリティ技術に関する国際会議  2012 

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  • マルチエージェントネットワークにおける代数的連結度計算のための新しい連続時間アルゴリズム

    電子情報通信学会非線形問題研究会  2012 

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  • 非負制約付き凸2次計画問題に対する修正乗法型更新アルゴリズムの大域収束性

    電子情報通信学会非線形問題研究会  2012 

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  • Some Properties of Extremal Points of Solution Curves for a Class of Nonlinear Equations

    電子情報通信学会非線形問題研究会  2012 

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  • 非負制約付き凸2次計画問題に対する修正乗法型更新アルゴリズム

    電子情報通信学会2012年総合大会  2012 

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  • 星グラフに辺を加えたグラフの代数的連結度最大性について

    電子情報通信学会2012年総合大会  2012 

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  • On the Rank of a Jacobian Matrix of a Class of Nonlinear Equations

    電子情報通信学会回路とシステム研究会  2012 

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  • Nonnegative Matrix Factorization のための修正乗法型更新アルゴリズムとその大域的収束性 -ダイバージェンス最小化の場合-

    電子情報通信学会回路とシステム研究会  2012 

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  • グラフラプラシアンの第2固有値を最大にする無向グラフ -平均次数が2以下の場合-

    電子情報通信学会回路とシステム研究会  2011 

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  • A Modified Multiplicative Update Algorithm for Euclidean Distance-Based Nonnegative Matrix Factorization and its Global Convergence

    第18回ニューラル情報処理に関する国際会議  2011 

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  • NMFに対する終了条件付き修正乗法型更新アルゴリズム

    平成23年度電気関係学会九州支部連合大会  2011 

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  • ある種のブロックグラフの次数保存クラスター係数極大性

    平成23年度電気関係学会九州支部連合大会  2011 

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  • ある種の正則グラフの代数的連結度極大性に関する一考察

    平成23年度電気関係学会九州支部連合大会  2011 

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  • On Topology of Networked Multi-Agent Systems for Fast Consensus

    2011年非線形理論とその応用に関する国際会議  2011 

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  • Controlling Clustering Coefficient of Graphs by Means of 2-Switch Method

    2011年非線形理論とその応用に関する国際会議  2011 

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  • Nonnegative Matrix Factorization のための修正乗法型更新アルゴリズムとその大域的収束性 -ユークリッド距離最小化の場合-

    電子情報通信学会非線形問題研究会  2011 

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  • 次数保存2辺張り替えに基づくクラスター係数の制御

    電子情報通信学会2011年総合大会  2011 

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  • ベイズ超解像におけるSIFTを用いたパラメタ推定手法の提案

    電子情報通信学会画像工学研究会  2011 

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  • シンプレックス法に基づく逐次部分最適化アルゴリズムの収束性について

    平成22年度電気関係学会九州支部連合大会  2010 

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  • 区分線形リカレントニューラルネットワークによる2値ベクトル系列の生成

    平成22年度電気学会 電子・情報・システム部門大会  2010 

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  • クラスター係数の最大値および極大値に関する考察

    電子情報通信学会非線形問題研究会  2010 

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Awards

  • 2021 IEEE International Conference on Progress in Informatics and Computing Best Paper Award

    2021.12   PIC-2021 Organizing Committee  

    Keiju Hayashi, Tsuyoshi Migita, Norikazu Takahashi

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  • Graph Golf 2021 General Graph Deepest Improvement Award

    2021.11   Graph Golf Organizer  

    Yoshiki Satotani, Norikazu Takahashi

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  • ベストティーチャー賞

    2021.3   岡山大学工学部  

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  • ベストティーチャー賞

    2018.3   岡山大学工学部  

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  • 特別賞(中国東北大学との学生交流への貢献)

    2018.3   岡山大学工学部  

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  • Honor Prize (for the winner of the NOLTA society logo design contest)

    2016.11   電子情報通信学会NOLTAソサイエティ  

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  • 貢献賞(編集)

    2015.9   電子情報通信学会NOLTAソサイエティ  

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    Country:Japan

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  • ベストティーチャー賞

    2014.3   岡山大学工学部  

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  • 2012年度IBISML研究会賞

    2013.7   電子情報通信学会情報論的学習理論と機械学習研究会  

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    Country:Japan

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  • 平成22年度九州大学工学講義賞

    2011.10   九州大学工学部  

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  • 平成12年度(第63回)学術奨励賞

    2001.3   電子情報通信学会  

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Research Projects

  • Consensus-Based Distributed Optimization Algorithms of Low Computational Cost and Their Applications to Machine Learning

    Grant number:21H03510  2021.04 - 2025.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    高橋 規一, 右田 剛史

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    Grant amount:\13520000 ( Direct expense: \10400000 、 Indirect expense:\3120000 )

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  • Development of Efficient Methods for Optimizing the Structure of Networked Systems Based on Various Measures

    Grant number:15K00035  2015.04 - 2018.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    Takahashi Norikazu

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    Grant amount:\4550000 ( Direct expense: \3500000 、 Indirect expense:\1050000 )

    We studied the problem of optimizing the network topology based on various measures such as the algebraic connectivity, the clustering coefficient, the betweenness centrality, the average shortest path length, and so on. We not only derived the algebraic connectivity maximizing (or locally maximizing) graphs, the clustering coefficient locally maximizing graphs, and the global clustering coefficient maximizing graphs through theoretical analysis, but also developed various algorithms for optimizing the network topology based on the betweenness centrality and the average shortest path length. We also developed some decentralized algorithms for computing the algebraic connectivity, and some fast methods for nonnegative matrix factorization to solve the problem of community detection.

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  • Topology optimization of network systems based on graph theory and dynamical systems theory

    Grant number:24560076  2012.04 - 2015.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    TAKAHASHI Norikazu

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    Grant amount:\5070000 ( Direct expense: \3900000 、 Indirect expense:\1170000 )

    We studied the problem of optimizing the network topology based on indices such as clustering coefficient, algebraic connectivity and average shortest path length. Not only some properties of the networks having optimal or locally optimal topologies were revealed by theoretical analysis, but also some algorithms that can generate networks with nearly optimal topologies were developed. We also studied some dynamics related problems such as the decentralized estimation of the algebraic connectivity, the convergence analysis of discrete-time recurrent neural networks, the analysis of the number of DC operating points in a certain nonlinear circuits, and the global convergence of iterative solution methods for nonnegative matrix factorization, and obtained many important results through both theoretical analysis and numerical experiments.

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  • Estimation of structural change and event occurrence by using the complex systems and its application to risk control and option evaluation

    Grant number:23310104  2011.04 - 2015.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    SHOZO Tokinaga, OONISHI Toshiro, ONO Hirotaka, TAKAHASHI Norikazu, NAKANISHI Makoto, MATSUNO Seigo, TAKAGI Noboru, IKEDA Yoshikazu

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    Grant amount:\19370000 ( Direct expense: \14900000 、 Indirect expense:\4470000 )

    This research attended to apply the estimation of structural change and event occurrence by using the complex systems and its application to risk control and option evaluation. Especially, we extend the theory of real option and Bayesian estimation for the analysis of complex system. In the final year of this research, we provided the result of research to other institutions. Namely, 1)Theory and practice for the investment and formation of relations among firms, 2) Development of software to analyze the complex system and installation to nother institutions, 3)Publications of result of researches in the journal of societies such as Institute of Electornics and Information Engineering in Japan.

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  • Generation of extremely ill-conditioned matrices and illconditoned circuits

    Grant number:23560472  2011 - 2013

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    NISHI TETSUO, TAKAHASHI Norikazu

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    Grant amount:\5330000 ( Direct expense: \4100000 、 Indirect expense:\1230000 )

    The quality of numerical algorithms can be evaluated by solving extremely ill-conditioned problems; For example, linear simultaneous equations having a coefficient matrix with extremely large condition number and nonlinear equations possessing infinitely many solutions. For this purpose we studied on the generation of extremely ill-conditioned matrices and on an upper bound of the condition number of a matrix and showed the possibility that the upper bound of the condition number derived by Guggenheimer, et al may approximately be achieved.
    We also investigate a nonlinear equation derived originally from transistor circuits and found some interesting properties of solution curve equations derived from it.

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  • Development of Fast Solution Methods based on Sequential Partial Optimization for Large Scale Convex Programming Problems

    Grant number:21560068  2009 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    TAKAHASHI Norikazu

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    Grant amount:\4160000 ( Direct expense: \3200000 、 Indirect expense:\960000 )

    We developed sequential partial optimization algorithms for fundamental continuous convex programming problems such as linear programs and convex quadratic programs, and evaluated their characteristics and efficiency through global convergence analysis and numerical experiments. We also carried out theoretical analysis and development of efficient algorithms for various optimization problems arising in the field of information and communication technology. To be more specific, we studied research issues such as efficient computation methods for nonnegative matrix factorization, optimal design methods for recurrent neural networks, maximizing clustering coefficient of complex networks, and optimization of the topology of multi-agent networks for fast consensus, and obtained many important results.

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  • Circuit- and graph-theoretic approach to the accuracy-guaranteed algorithm for a general-purpose circuit simulator

    Grant number:20560374  2008 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    NISHI Tetsuo, TAKAHASHI Norikazu, NAKAYA Yuusuke

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    Grant amount:\4420000 ( Direct expense: \3400000 、 Indirect expense:\1020000 )

    Main results are the following three items :
    1)By using the accuracy-guaranteed algorithm developed in our laboratory we numerically proved that the specified two-transistor circuit proposed previously by other researchers has surely five solutions. As the result we see that the maximum number of solutions of two-transistor circuits is equal to or greater than five. 2) On the generation of an extremely ill-conditioned matrix 2.1) we clarified the relation between the singular values of the matrix and an upper bound of the condition number, 2.2) we proposed a new simple method to generate an extremely ill-conditioned matrix, 2.3) we proposed a method to generate a matrix with more desirable properties as the bench mark matrices for the accuracy-guaranteed algorithm. 3) We proposed several methods to estimate the upper bound of the errors of the solutions obtained by circuit analysis program such as SPICE.

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  • Modeling of Diffusion Processes and Self-organization based on the Complex Systems and their Applications to Systematic Risk Control

    Grant number:19310099  2007 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    TOKINAGA Shozo, IWAMOTO Seiichi, NAKAI Wataru, TAKAHASHI Norikazu, MORIYASU Hiroshi, IKEDA Yoshikazu, TAN Kangrong, TAKAGI Noboru

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    Grant amount:\19500000 ( Direct expense: \15000000 、 Indirect expense:\4500000 )

    In this research, we published theoretical and practical results in many conferences and journals of academic societies, and we also subjective experiences reviewing from domestic and foreign researchers. We realized many publications of papers and books as well as practical software systems concerning about the Complex Systems and Risk Management which is the main topics of this research through valuable discussion with specialists of the underlying topics. At the same time, we provided efficient software to many manufactures managing supply chains, and also to financial institutions who are devoted to customer information management. Overview of the research is summarized as follows.
    (1) We provided many seminar for the manufactures and financial institutions about the investment and supply chains.
    (2) We aggregate the current result and problems still remained to be solved.
    (3) We developed analytical software about the complex systems and risk management, and installed to another systems.
    (4) The results of this research were widely published through the accepted papers in academic societies such as Operations Research Society of Japan, The Institute of Electronics, Information and Communication Engineering and The Japan Society of Information Processing.
    (5) The result of this research was finally included in a book which was fully supported by the grant for publication of the Japan Society for the Promption of Science.

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  • Development of Learning Theory based on Information Measure

    Grant number:19300051  2007 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    TAKEUCHI Junichi, TAKAHASHI Norikazu, JITSUMATSU Yutaka

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    Grant amount:\18590000 ( Direct expense: \14300000 、 Indirect expense:\4290000 )

    We studied machine learning, information theory, and other related topics from a unified viewpoint of minimum description length principle (MDL principle). In particular, we obtained the new sight on the relation between geometrical structure of tree models and stochastic complexity (SC) and that between communication channel capacity and SC. We also studied ensemble learning and kernel method, and obtained efficient learning method for them. Further, on the basis of the fundamental knowledge obtained in this research, we proposed new learning based methods for incident detection in network security, universal portfolio, super resolution etc., and showed their efficiency.

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  • Research on the design of SAW filters for a duplexer based on network theory

    Grant number:16560339  2004 - 2006

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    NISHI Tetsuo, OGATA Masato

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    Grant amount:\3500000 ( Direct expense: \3500000 )

    The aim of this research is to develop the design method of SAW filters, which is usually used in the duplexer of portable phones. A SAW element is a kind of electro-mechanical transducers utilizing the surface acoustic wave, can be manufactured in very small size, and has very high Q (about 800). The characteristics of SAW elements can be modelled by distributed-constant circuits. The use of SAW elements enables high Q bandpass filters with sharp cutoff characteristics for 800Mhz frequency band. The filter has to possess large attenuation at higher frequency band (or lower frequency band) of the passband due to the requirement for duplexers. We use the circuit-theoretic approach for the design.
    1. Let T(s)=N(s)/D(s) be a transfer function of a SAW filter. We proposed a design method of filter characteristics T(s) with equiripple attenuation characteristics in the stop band and has the maximally flat passband characteristics.
    2. We proposed a design method of SAW filters, (1) which has symmetrical structure, (2) which are composed not only of SAW elements but also lumped-constant inductances. Then the network is modelled as a mixed lumped-and distributed-network and therefore is difficult to analyze and design it.
    The π-type or Y-type inductances are placed with a conventional SAW ladder filter. We investigated in detail the effects of inserted inductances for the attenuation frequency bands and showed that the Y-type is better for the analysis and synthesis.

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  • カオスに基づいたi.i.d.2値系列によるストリーム暗号システム

    Grant number:16016269  2004 - 2005

    日本学術振興会  科学研究費助成事業 特定領域研究  特定領域研究

    香田 徹, 大濱 靖匡, 高橋 規一, 實松 豊

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    Grant amount:\11200000 ( Direct expense: \11200000 )

    従来,有限体理論に基づいた整数値の擬似乱数生成法が多用されている.一方,確率論ではコイン投げの数学的モデルであるi.i.d.(independent and identically distributed)2値系列が最も重要である.先に本研究代表者は,実数値系列に基づくi.i.d.2値系列生成法をカオス理論で明らかにし,i.i.d,2値系列が情報通信分野で必須の系列として有用であることを示した.本研究は,統計学・確率論基準の暗号強度評価法の確立を目的に遂行したものであり,その主要結果は以下の三点である.(1)i.i.d.2値系列を得るための十分条件を与え、それが可換な有理関数写像であるヤコビ楕円関数写像を含む広いクラスの1次元写像で生成される実数値系列の独立性判定にも適用可能であることを明らかにした.この結果は国際的に認知され,IEEEの会誌特集号の招待論文に纏められているので,IEEEの相当数の会員が知ることとなった.また,楕円暗号がWeierstrass型楕円関数とその微分間の代数的関係式である平面曲線で規定されることに鑑み,ヤコビ楕円関数とその微分,2階微分間を規定する(x,y,z)-空間曲線とその上の力学系及び各軸の1次元射影写像を定義した.その結果,三種類の射影写像は上記十分条件を満たすので,曲線上の実数値軌道ベクトルの2進展開は3次元i.i.d.2値ベクトル系列となることが明らかとなった.このことは,高精細なカラー画像用ストリーム暗号システムが容易に実現できることを示唆している.(2)ブロック暗号のDES(1ブロックからそれへの非線形写像をn段繰り返す.標準はn=16)の強度評価は暗号分野では古典的であるが基本テーマの一つである.偏りのある平文(偏りのあるi.i.d.2値系列も可)を入力するという前提だけの暗号文単独攻撃耐性基準のブロック暗号強度評価法を2種類与えた.これらは,標準DESの解読には,数十テラの英文Ascii平文と暗号文対を必要とする,従来の評価法とは全く異なる.具体的には,数メガの暗号文ビット間の入出力関係頻度表だけで4,6段DESでは全鍵が検出可能であるとの結果を得た.(3)米国の研究グループ提案のElgamal型公開鍵システムを模倣した可換多項式で生成された実数値カオス系列に基づくシステムの公開鍵は秘密鍵を露呈していることをカオス理論により示した.上記研究成果から明らかなように,カオス理論に基づく暗号強度評価法の研究は国策上今後も是非遂行されるべきである。

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  • 多層セルラニューラルネットワークの最適設計手法に関する研究

    Grant number:15760268  2003 - 2004

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    高橋 規一

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    Grant amount:\1300000 ( Direct expense: \1300000 )

    本年度の成果は以下の通りである。
    1.1次元2層セルラニューラルネットワーク(CMN)の安定パターンの特徴付けに関する前年度の成果をまとめ、国際会議2004 IEEE International Midwest Symposium on Circuits and Systemsにおいて発表した。
    2.一般化固有値最小化に基づくCNN連想記憶設計法が実は線形計画問題に帰着されることを証明し、線形計画法に基づくCNN連想記憶設計法を提案した。提案手法は一般化固有値最小化に基づく方法に比べて設計時間が大幅に短く、従来法と同等の想起性能を示すことを数値実験によって明らかにした。また、大規模ランダムパターンを用いた実験により、提案手法は、外積法、射影学習則、固有構造法などの従来法よりも優れた想起性能を示すことを明らかにした。
    3.1次元離散時間CNNの安定性を理論的に解析し、任意の初期条件に対してCNNが必ず平衡状態に収束するための必要十分条件を導出した。
    4.サポートベクトルマシン(SVM)の学習法としてよく用いられる分割法の収束性を解析し、変数選択に関する非常に緩い条件の下で分割法の解が必ず最適解に収束することを証明した。また、非線形回帰のためのSVMの効率的学習法について検討し、分割法に基づく新しい学習アルゴリズムを提案した。提案アルゴリズムの有効性を数値実験によって示した。

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  • Theoretical study on the number of solutions and the stability on transistor circuits

    Grant number:13650414  2001 - 2003

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    NISHI Tetsuo, OGATA Masato, TAKAHASHI Norikazu, NISHI Tetsuo

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    Grant amount:\3200000 ( Direct expense: \3200000 )

    This study aims to pursue two subjects on nonlinear active circuits including transistor circuits. One is to investigate the maximum number of solutions of transistor circuits under the prescribed topology. This problem was proposed by the Technical Committee on Nonlinear Circuits and Systems of the IEEE CAS Society several years ago.. The other is to investigate the stability conditions for general active circuits including transistor circuits. The main results of this research are summarized as follows:
    1.We showed that the algebraic equations which have two variables and whose nonlinear terms are exponential functions of the variables have at most five solutions. This type of equations come from transistor circuits.. The above result show that the well-known conjecture does not hol in general.
    2.We give some sufficient conditions for the denominator polynomial of active RC circuits including transistor circuits not to yield negative coefficients due to parasitic elements. This result then shows some conditions for stability of this class of circuits.
    3.We give the necessary and sufficient conditions for a one-dimensional discrete-time cellular neural network, which is a class of active analog circuits.
    4.We give the necessary and sufficient condition for the second-order differential equations to be globally stable.

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  • 完全安定セルラーニューラルネットワークの最適設計に関する研究

    Grant number:13750358  2001 - 2002

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    高橋 規一

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    Grant amount:\1400000 ( Direct expense: \1400000 )

    本年度の研究成果は次の通りである。
    1.セルラーニューラルネットワーク(CNN)による連想記憶回路の構成法について検討し、ある種の最適化手法に基づくCNN設計を提案した。提案手法は、従来手法に比べて理論的裏付けがしっかりしているだけでなく、設計手続きが簡単であり、MATLAB等の数値計算ソフトを利用すればCNNのパラメータが簡単に求められるという利点もある。アルファベット26文字に提案手法と従来法を適用した結果、すべての場合において従来法よりも高い平均想起確率が達成されることが確認された。
    2.遅延特性を有するCNNの完全安定性に関する新たな十分条件を導出した。この結果は、CNNの完全安定性に関してこれまでに得られているいくつかの結果の一般化になっている。また、2個のセルから構成されるCNNの完全安定性を解析し、ある仮定の下でそれが完全安定であるための必要十分条件を導出した。
    3.直線上に配置された多数のセルから構成される1次元離散時間CNNが任意の初期条件に対して必ず平衡状態に収束するための必要十分条件を導出した。
    4.DogaruとChuaによって提案されたユニバーサルCNNセルの解析および設計に関する研究を行った。具体的には、最急降下法に基づく効率的なユニバーサルCNNセルの設計法を提案し、その有効性を数値実験によって確認した。ユニバーサルCNNセルでは、多数の絶対値関数を用いることによって複雑な入出力関係が実現されるが、回路構造を簡単にするために絶対値関数の個数をできるだけ少なくする必要がある。数値実験の結果、提案手法においては、所望の入出力関係を実現するのに必要な絶対値関数の個数が各セルの結合数に比例することが明らかになった。

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  • Discrimination theory of wavelet filters with learning ability

    Grant number:11558039  1999 - 2002

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    NIIJIMA Koichi, TAKANO Shigeru, KUZUME Koichi, OKADA Yoshihiro

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    Grant amount:\12900000 ( Direct expense: \12900000 )

    Wavelet filters with learning ability indicate lifting wavelet filters proposed by Sweldens who is a researcher at Lucent Technology in USA. The lifting wavelet filters are consist of biorthogonal analysis and synthesis filters. A signal is decomposed into lowpass and highpass components using the analysis filter, and the original signal can be reconstructed from the lowpass and highpass components using the synthesis filter. This means that the original signal is equivalent to the decomposed lowpass and highpass components. The lifting wavelet filters are constructed by adding lifting filters to biorthogonal wavelet filters. The lifting filter contains free parameters which can be determined adaptive to signals and images.
    In our research, we proposed several learning methods of the free parameters adaptive to specific parts of signals and images, and established a discrimination theory for extracting pieces similar to the specific parts. We also presented an impulse noise reduction method based on our learning method. Furthermore, we proposed a fast simplification algorithm for generating 3D surfaces by using an idea of multiresolution analysis of wavelets.

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  • セルラーニューラルネットワークの完全安定性解析

    Grant number:11750330  1999 - 2000

    日本学術振興会  科学研究費助成事業 奨励研究(A)  奨励研究(A)

    高橋 規一

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    Grant amount:\1100000 ( Direct expense: \1100000 )

    本年度の研究実績は以下の通りである.
    1.遅延特性を有するセルラーニューラルネットワーク(Cellular Neural Network,以下CNN)が完全安定であるための新しい十分条件と,他の研究者によって予想された完全安定条件に対する反例をまとめ,IEEE Transactions on Circuits and Systems-Iに発表した.
    2.CNNに対する二つの既存の完全安定条件が同一原理で導出できることを示すとともに,これらを統一的に扱うことのできる新しい十分条件を導出した.この結果は,国際会議2000 International Symposium on Nonlinear Theory and its Applicationsにおいて発表された.また,遅延特性を有するCNNに対しても同様の考察を行い,新しい十分条件を導出した.
    3.与えられた平衡点集合を実現するCNNの設計問題は,連想記憶やパターン認識への応用において基本的かつ重要な問題である.これまでに,特異値分解を利用したCNN設計法が提案されているが,その方法では完全安定性が保証されないという問題があった.そこで本研究では,結合を対称にすることにより完全安定性を保証する新しい設計法を提案した.しかしながら,まだ問題点も多く,提案法に改良を加えていく必要がある.
    4.2個のセルからなるCNNのダイナミクスを詳細に解析し,ある仮定の下で,CNNが完全安定であるための十分条件およびリミットサイクルが存在するための十分条件を新たに与えた.その過程で,2個のセルからなるCNNの完全安定性に関する従来の結果に誤りがあることを明らかにした.この成果は,平成13年度に国際会議等で発表したいと考えている.

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  • Discovery of structure from color images by entropy minimization learning of neural networks

    Grant number:10480076  1998 - 2001

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

    NIJIMA Koichi, TAKANO Shigiru, TAKAHASHI Norikazu, OKADA Yoshihiro

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    Grant amount:\10300000 ( Direct expense: \10300000 )

    Neural networks play an important role in this research. In order to discover the structure that characterizes images, we need to study learning methods for neural networks and to analyze the behavior of the learned neural network. It is required to study the classification and recognition ability of the neural network. We must find rules from the learned neural network. Simplification of 3D images for inputting in the neural network is also an important research subject.
    To resolve such problems, we studied various learning methods as well as the entropy minimization learning technique for neural networks and the behavior of cellular neural networks. And we applied the obtained results to image classification and rule extraction. We proposed a method for finding a hidden image from two similar images by combining the entropy minimization learning technique of the neural network with a wavelet theory, which is a main theme of this research. For discovering the structure of 3D models using a neural network, we studied simple surface generation algorithms for obtaining vertices which are input data of the neural network.

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