Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： 10.14923/transfunj.2022JAI0001

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

DOI： 10.34385/proc.76.D2L-23

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

DOI： 10.1109/emcsipi50001.2023.10241637

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electronics, Information and Communications Engineers (IEICE)  

DOI： 10.1587/transinf.2022edl8098

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.neunet.2023.05.013

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

DOI： 10.1109/tencon55691.2022.9977529

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

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

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

DOI： 10.1109/PIC50277.2020.9350816

J-GLOBAL

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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

J-GLOBAL

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

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

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

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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

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

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.2299/jsp.23.41

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

DOI： 10.1016/j.jcss.2018.10.006

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

DOI： 10.1109/ICCNC.2019.8685549

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

DOI： 10.1109/TENCON.2018.8650418

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

DOI： 10.1109/LCSYS.2018.2843679

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

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

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

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

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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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

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.

DOI： 10.1007/s10589-013-9593-0

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

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

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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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

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.

DOI： 10.1587/nolta.4.430

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

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.

DOI： 10.1109/EST.2012.32

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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

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.

DOI： 10.1587/nolta.3.301

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

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

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.

DOI： 10.1007/978-3-642-24958-7_76

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Institute of Electronics, Information and Communication Engineers  

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.

DOI： 10.1587/nolta.2.432

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Institute of Electronics, Information and Communication Engineers  

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.

DOI： 10.1587/nolta.2.443

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Publisher：Committee of Joint Conference of Electrical, Electronics and Information Engineers in Kyushu  

DOI： 10.11527/jceeek.2011.0_393

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Publisher：Committee of Joint Conference of Electrical, Electronics and Information Engineers in Kyushu  

DOI： 10.11527/jceeek.2011.0_394

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Publisher：Committee of Joint Conference of Electrical, Electronics and Information Engineers in Kyushu  

DOI： 10.11527/jceeek.2011.0_77

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

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.

DOI： 10.1016/j.nonrwa.2010.05.007

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DOI： 10.1109/CNNA.2010.5430264

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

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).

DOI： 10.1109/ECCTD.2009.5275108

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

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.

DOI： 10.1109/TCSI.2008.925828

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

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.

DOI： 10.1109/TNN.2007.915116

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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.

DOI： 10.1109/TCSI.2008.925828

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

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.

DOI： 10.1109/ICACTE.2008.48

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

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.

DOI： 10.1007/978-3-540-87732-5_74

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

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.

DOI： 10.1109/IJCNN.2008.4633836

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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.

DOI： 10.1109/ISCAS.2007.378101

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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.

DOI： 10.1093/ietfec/e89-a.12.3963

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

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.

DOI： 10.1109/TNN.2006.880584

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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.

DOI： 10.1093/ietfec/e89-a.10.2825

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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.

DOI： 10.1093/ietfec/e89-a.10.2795

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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.

DOI： 10.1109/TCSII.2006.876466

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER-VERLAG BERLIN  

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.

DOI： 10.1007/11893028_92

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

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

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

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

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

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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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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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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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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DOI： 10.1109/MWSCAS.2004.1354009

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

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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DOI： 10.1007/978-3-540-28647-9_79

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

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

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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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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

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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Language：English   Publisher：Kyushu University  

DOI： 10.15017/1525450

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

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

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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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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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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DOI： 10.1109/81.852931

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

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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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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Language：English   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

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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Publisher：Kyushu University  

DOI： 10.15017/1474975

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

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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Language：Japanese   Publisher：電子情報通信学会  

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Other Link： http://id.ndl.go.jp/bib/029633374

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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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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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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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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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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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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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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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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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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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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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Language：English   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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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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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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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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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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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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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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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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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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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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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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Language：Japanese   Publisher：Information Processing Society of Japan (IPSJ)  

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/

Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Language：Japanese   Publisher：The Institute of Electronics, Information and Communication Engineers  

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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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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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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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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Language：English   Publisher：Kyushu University  

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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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