## About

91

Publications

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295

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Citations since 2017

Introduction

Yuchi Kanzawa currently works at the Department of Communications Engineering, Shibaura Institute of Technology. Yuchi does research in Data Mining including fuzzy clustering. Their most recent publication is 'Semi-supervised Fuzzy c-Means Algorithms by Revising Dissimilarity/Kernel Matrices.'

**Skills and Expertise**

Additional affiliations

April 2017 - present

## Publications

Publications (91)

This study presents a generalized Tsallis entropy-based fuzzy c -means (GTFCM) clustering algorithm. Furthermore, the results of this study show that the behavior of GTFCM, at an infinity point of the fuzzy classification function, is similar to that of some conventional clustering algorithms. This result implies that such behavior is determined by...

Clustering for categorical multivariate data is an important task for summarizing co-occurrence information that consists of mutual affinity among objects and items. This work focus on two fuzzy clustering methods for categorical multivariate data. One of the serious limitations for these methods is the local optimality problem. In this work, an al...

In many fuzzy clustering algorithms, the KL-divergence-regularized method based on the Gaussian mixture model, fuzzy classification maximum likelihood, and a fuzzy mixture of Student’s-t distributions have been proposed for cluster-wise anisotropic data, whereas more other types of fuzzification technique have been applied to fuzzy clustering for c...

Various fuzzy clustering algorithms have been proposed for vectorial data. However, these methods have not been applied to time-series data. This paper presents three fuzzy clustering algorithms for time-series data based on dynamic time warping (DTW). The first algorithm involves Kullback–Leibler divergence regularization of the DTW k-means object...

In this paper, the q-divergence-regularized Bezdek-type fuzzy clustering approach is proposed for categorical multivariate data. Because the approach proposed here reduces to the conventional methods via appropriate control of the fuzzification parameters, it is considered as a generalization. Further, numerical experiments were conducted to show t...

Although recommendation systems are the most powerful tool to help people choose items, a higher recommendation accuracy is required to satisfy the needs of the people. Motivated by this requirement, this study proposes a novel collaborative filtering (CF) algorithm, which is the underlying technology of a recommendation system. It filters items fo...

This study shows that a generalized fuzzy c -means (gFCM) clustering algorithm, which covers both standard and exponential fuzzy c -means clustering, can be constructed if a given fuzzified function, its derivative, and its inverse derivative can be calculated. Furthermore, our results show that the fuzzy classification function for gFCM exhibits a...

In this study, Tsallis entropy-regularized Bezdek-type fuzzy c-means clustering method is proposed. Because the proposed method reduces to four conventional fuzzy clustering methods by appropriately controlling fuzzification parameters, the proposed method is considered to be their generalization. Through numerical experiments, this generalization...

In this study, we present a fuzzy counterpart to the probabilistic latent semantic analysis (PLSA) approach. It is derived by solving the optimization problem of Tsallis entropy-penalizing free energy of a pseudo PLSA model by using a modified i.i.d. assumption. This derivation is similar to that of the conventional fuzzy counterpart of the PLSA, w...

This study shows that a general regularized fuzzy c -means (rFCM) clustering algorithm, including some conventional clustering algorithms, can be constructed if a given regularizer function value, its derivative function value, and its inverse derivative function value can be calculated. Furthermore, the results of the study show that the behavior...

This study presents a fuzzy clustering algorithm for classifying spherical data based on q -divergence. First, it is shown that a conventional method for vectorial data is equivalent to the regularization of another conventional method using q -divergence. Next, based on the knowledge that q -divergence is a generalization of Kullback-Leibler (KL)-...

In this study, a collaborative filtering method that uses fuzzy clustering and is based on q -divergence is proposed for categorical multivariate data. The results of experiments conducted on an artificial dataset indicate that the proposed method is more effective than the conventional one if the number of clusters and the initial setting are adeq...

This paper presents two fuzzy clustering algorithms for categorical multivariate data based on q -divergence. First, this study shows that a conventional method for vectorial data can be explained as regularizing another conventional method using q -divergence. Second, based on the known results that Kullback-Leibler (KL)-divergence is generalized...

In this paper, a power-regularization-based fuzzy clustering method is proposed for spherical data. Power regularization has not been previously applied to fuzzy clustering for spherical data. The proposed method is transformed to the conventional fuzzy clustering method, entropy-regularized fuzzy clustering for spherical data (eFCS), for a specifi...

In this paper, a clustering algorithm for relational data based on q -divergence between memberships and variables that control cluster sizes is proposed. A conventional method for vectorial data is first presented for interpretation as the regularization of another conventional method with q -divergence. With this interpretation, a clustering algo...

Various fuzzy co-clustering methods have been proposed for collaborative filtering; however, it is not clear which method is best in terms of accuracy. This paper proposes a recommender system that utilizes fuzzy co-clustering-based collaborative filtering and also evaluates four fuzzy co-clustering methods. The proposed system recommends optimal i...

Semi-supervised clustering uses partially labeled data, as often occurs in practical clustering, to obtain a better clustering result. One approach uses hard constraints which specify data that must and cannot be within the same cluster. In this chapter, we propose another approach to semi-supervised clustering with soft pairwise constraints. The c...

In this study, a Bezdek-type fuzzified possibilistic clustering algorithm for spherical data (bPCS), its kernelization (K-bPCS), and spectral clustering approach (sK-bPCS) are proposed. First, we propose the bPCS by setting a fuzzification parameter of the Tsallis entropy-based possibilistic clustering optimization problem for spherical data (tPCS)...

The present study proposes two types of powerregularized fuzzy c-means (pFCM) clustering algorithms with a fuzzification parameter less than one, which supplements previous work on pFCM with a fuzzification parameter greater than one. Both the proposed methods are essentially identical to each other, but not when fuzzification parameter values are...

In this study, two co-clustering algorithms based on Bezdek-type fuzzification of fuzzy clustering are proposed for categorical multivariate data. The two proposed algorithms are motivated by the fact that there are only two fuzzy co-clustering methods currently available - entropy regularization and quadratic regularization - whereas there are thr...

This paper proposes three modifications for the maximizing model of spherical Bezdek-type fuzzy c -means clustering (msbFCM). First, we use multi-medoids instead of centroids (msbFMMdd), which is similar to modifying fuzzy c -means to fuzzy multi-medoids. Second, we kernelize msbFMMdd (K-msbFMMdd). msbFMMdd can only be applied to objects in the fir...

In this paper, four possibilistic clustering methods are proposed. First, we propose two possibilistic clustering methods for spherical data — one based on Shannon entropy, and the other on Tsallis entropy. These methods are derived by subtracting the cosine correlation between an object and a cluster center from 1, to obtain the object-cluster dis...

In this study, a maximizing model of Bezdek-like spherical fuzzy c -means clustering is proposed, which is based on the regularization of the maximizing model of spherical hard c -means. Such a maximizing model was unclear in Bezdek-like method, whereas other types of methods have been investigated well both in minimizing and maximizing model. Usin...

The present study proposes an algorithm for sequential cluster extraction using power-regularized possibilistic c-means (pPCM). First, pPCM is derived in a similar manner to two types of entropy-regularized possibilistic c-means (ePCM) derivations, where a power function is utilized instead of the negative entropy in ePCM. The cluster fusion with p...

In this study, two clustering frameworks are proposed based on a maximizing model of spherical Bezdek-type fuzzy clustering are proposed. One using possibilistic c-means, and the other using multi-medoids. In each framework, the basic model and its kernelization are presented, along with an appropriate spectral clustering technique. Kernelization a...

In this study, a maximizing model of Bezdek-like spherical fuzzy c-means clustering is proposed, which is based on the regularization of the maximizing model of spherical hard c-means. Such a maximizing model was unclear in Bezdek-like method, whereas other types of methods have been investigated well both in minimizing and maximizing model. Using...

In this paper, two linear fuzzy clustering algorithms are proposed for relational data based on kernel fuzzy c-means, in which the prototypes of clusters are given by lines spanned in a feature space defined by the kernel which is derived from a given relational data. The proposed algorithms contrast the conventional method in which the prototypes...

In this paper, two types of fuzzy co-clustering algorithms are proposed. First, it is shown that the base of the objective function for the conventional fuzzy co-clustering method is very similar to the base for entropy-regularized fuzzy nonmetric model. Next, it is shown that the non-sense clustering problem in the conventional fuzzy co-clustering...

In this study, five co-clustering algorithms based on Bezdek-type fuzzification of fuzzy clustering are propsoed for categorical multivariate data. The algorithms are motivated the fact that, there are only two fuzzy co-clustering methods - entropy-regularization and quadratic regularization - whereas there are three fuzzy clustering methods for ve...

Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β - spread transformation was...

In this paper, the quadratic regularized and standard fuzzy c-means clustering algorithms (qFCM and sFCM) are generalized with respect to hard c-means (HCM) regularization. First, qFCM is generalized from quadratic regularization to power regularization. The relation between this generalization and sFCM is then compared to the relation between othe...

Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β -spread transformation was...

In this paper, some imputation strategies are compared in the point that the block diagonal part of the augmented dissimilarity matrix must be filled in for FNM-based and RFCM-based fuzzy co-clustering by entropy regularization, By numerical experiment, the eRFCM-based method with the minimax version of the strategy of the triangle inequality-based...

In this paper, three linear fuzzy clustering algorithms are proposed for relational data based on kernel fuzzy c-means, in which the prototypes of clusters are given by lines spanned in a feature space denned by the kernel which derived from a given relational data. The proposed algorithms contrast the conventional method in which the prototypes of...

In this paper, some fuzzy clustering methods are proposed for relational data which represents the dissimilarity for triples of data points. One method is based on the fuzzy nonmetric model and the other is on the relational fuzzy c-means. Each method has two options of fuzzification; the standard and the entropy-regularization. Through some numeri...

In this paper, an entropy-regularized fuzzy clustering approach for non-Euclidean relational data and indefinite kernel data is developed that has not previously been discussed. It is important because relational data and kernel data are not always Euclidean and positive semi-definite, respectively. It is theoretically determined that an entropy-re...

In this paper, some types of fuzzy co-clustering algorithms are proposed. First, it is shown that the common base of the objective function for quadratic-regularized fuzzy co-clustering and entropy-regularized fuzzy co-clustering is very similar to the base for quadratic-regularized fuzzy nonmetric model and entropy-regularized fuzzy nonmetric mode...

While explicit mapping is generally unknown for kernel data analysis, its inner product should be known. Although we proposed a kernel fuzzy c-means algorithm for data with tolerance, cluster centers and tolerance in higher dimensional space have not been seen. Contrary to this common assumption, explicit mapping has been introduced and the situati...

In this paper, two types of semi-supervised fuzzy cmeans algorithms are proposed. One feature of proposed algorithms is that they are based on an entropyregularized fuzzy c-means clustering algorithm, while conventional algorithms are based on standard fuzzy c-means. Another feature of proposed algorithms is that the membership updating equation ca...

In this paper, we investigate three types of c-means clustering algorithms with a conditionally positive definite kernel. One is based on hard c-means, and the others are based on standard and entropy-regularized fuzzy c -means. First, based on a conditionally positive definite kernel describing a squared Euclidean distance between data in the feat...

We propose two approaches for semi-supervised FCM with soft pairwise constraints. One applies NERFCM to the revised dissimilarity matrix by pairwise constraints. The other applies K-FCM with a dissimilarity-based kernel function, revising the dissimilarity matrix based on whether data in the same cluster may be close to each other or the data in th...

Clustering - defined as an unsupervised data-analysis classification transforming real-space information into data in pattern space and analyzing it - may require that data be represented by a set, rather than points, due to data uncertainty, e.g., measurement error margin, data regarded as one point, or missing values. These data uncertainties hav...

This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity between each d...

An explicit mapping is generally unknown for kernel data analysis but their inner product should be known. Though kernel fuzzy c-means algorithm for data with tolerance has been proposed by the authors, the cluster centers and the tolerance in higher dimensional space have been unseen. Contrary to this common assumption, an explicit mapping has bee...

This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity
between each d...

In this paper, some semi-supervised clustering methods are proposed with two types of pair constraints: two data have to be
together in the same cluster, and two data have to be in different clusters, which are classified into two types: one is based
on the standard fuzzy c-means algorithm and the other is on the entropy regularized one. First, the...

This paper presents a new clustering algorithm, which is based on entropy regularized fuzzy c-lines, can treat data with some errors. First, the tolerance is formulated and introduce into optimization problem of clustering. Next, the problem is solved using Karush-Kuhn-Tucker conditions. Last, the algorithm is constructed based on the results of so...

In recent years, data from many natural and social phenomena are accumulated into huge databases in the world wide network of computers. Thus, advanced data analysis techniques to get valuable knowledge from data using computing power of today are required. Clustering is one of the unsupervised classification technique of the data analysis and both...

This paper presents a new clustering algorithm ,which is based on fuzzy c-lines, can treat data with some errors. First, the tolerance is formulated and introduce into optimization problem of clustering. Next, the problem is solved using Karush-Kuhn-Tucker conditions. Last, the algorithm is constructed based on the results of solving the problem. S...

In this paper, two fuzzy classification functions of fuzzy c-means for data with tolerance are proposed. First, two clustering algorithms for data with tolerance are introduced. One is based on the standard method and the other is on the entropy-based one. Second, the fuzzy classification function for fuzzy c-means without tolerance is discussed as...

In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions
are proposed.
First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy
classification function for fuzzy c-means without tolerance using kernel functions is...

In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Non-linear boundary of clusters can be easily found by using the kernel functi...

In this paper, the fuzzy classification functions of the entropy regularized fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel fun...

In this paper, two fuzzy classification functions of fuzzy c-means for data with tolerance are proposed. First, two clustering algorithms for data with tolerance are introduced. One is based on the standard method and the other is on the entropy-based one. Second, the fuzzy classification function for fuzzy c-means without tolerance is discussed as...

In this paper, two new clustering algorithms are proposed for data with some errors. In any of these algorithms, the error is interpreted as one of decision variables - called ldquotolerancerdquo - of a certain optimization problem like the previously proposed algorithm, but the tolerance in new methods is determined by the new introduced penalty t...

In this paper, two new clustering algorithms are proposed for the data with some errors. In any of these algorithms, the error is interpreted as one of decision variables — called “tolerance” — of a certain optimization problem like the previously proposed algorithm, but the tolerance is determined based on the opposite criterion to its correspondi...

In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clusteri...

In this paper, the objective is to derive with guaranteed accuracy all solutions of a finite-dimensional nonlinear equation within a certain range. In order to derive all solutions, it is important to extract efficiently the regions in which no solution exists. A new method is proposed in which nonexistence of solutions in a given region is judged...

An algorithm for arbitrarily minimizing the width of the interval which does not contain the solutions from the interval which contains the solutions of equations using nonlinear functions in which the dimension of the definition domain is greater than the dimension of the value range is proposed in this paper. In addition, the effectiveness of the...

This paper proposes an algorithm which can derive all solutions with guaranteed accuracy for equations including a nonlinear function, with the dimension of the domain larger than the dimension of the range. It is mathematically shown that the proposed algorithm is completed in a finite number of steps under an appropriate condition. The effectiven...

this paper as the limit of numerFfi# apprFfi h topr ve the existence ofsingular solutions. In the field ofengineerWSfi we needpr ving the existence ofsingular solutions to avoid them. For example, electrFWS circtr must be designed to have no singular operF2Ffi points. We have the case that ar2fi electrTFfl circtr hassingular operWWS2 points while t...

SUMMARY This paper presents a method of calculating an interval including a bifurcation point. Turning points, simple bi- furcation points, symmetry breaking bifurcation points and hys- teresis points are calculated with guaranteed accuracy by the extended systems for them and by the Krawczyk-based interval validation method. Taking several example...

This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based...

A new concept of “an approximate singular solutioll” is defincd as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations.
A numerical method is presented for proving the existence of approximate singular solutions of nonlinear equations with guaranteed accuracy. A few numerical e...