■Faculty | Department of Informatics / Graduate School of Science and Engineering Research |

■Position | Lecturer |

■Degree | |

■Commentator Guide | https://www.kindai.ac.jp/meikan/479-hamasuna-yukihiro.html |

■URL | |

Last Updated :2020/09/30

- Informatics, Sensitivity (kansei) informatics
- Informatics, Soft computing
- Informatics, Intelligent informatics
- Informatics, Information theory

- Data Science, Machine Learning, Soft Computing, Clustering

- k-Medoids Clustering Based on Kernel Density Estimation and Jensen-Shannon Divergence, Yukihiro Hamasuna, Yuto Kingetsu, Shusuke Nakano, The 16th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2019), The 16th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2019), Sep. 2019 , Refereed
- Cluster Validity Measures Based Agglomerative Hierarchical Clustering for Network Data, Yukihiro Hamasuna, Shusuke Nakano, Ryo Ozaki, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), 23(3), 577 - 583, May 2019 , Refereed
- Cluster Validity Measures for Network Data., Yukihiro Hamasuna, Daiki Kobayashi, Ryo Ozaki, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), 22(4), 544 - 550, Jul. 2018 , Refereed
- Fuzzified Even-Sized Clustering Based on Optimization., Kei Kitajima, Yasunori Endo, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), 22(4), 537 - 543, Jul. 2018 , Refereed
- On Fuzzified Even-sized Clustering Based on Optimization, Kei Kitajima, Yasunori Endo, Yukihiro Hamasuna, The 14th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2017), The 14th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2017), Oct. 2017 , Refereed
- On Edge Penalty Based Hard and Fuzzy c-Medoids for Uncertain Networks, Yukihiro Hamasuna, Yasunori Endo, The 14th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2017), The 14th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2017), Oct. 2017 , Refereed
- Two Roles of Cluster Validity Measures for Clustering Network Data, Yukihiro Hamasuna, Ryo Ozaki, Yasunori Endo, The 2017 conference of the International Federation of Classification Societies (IFCS2017), The 2017 conference of the International Federation of Classification Societies (IFCS2017), Aug. 2017 , Refereed
- Comparison of Trace of Fuzzy Covariance Matrix with Its Kernelization in Cluster Validity Measures based x-means, Yukihiro Hamasuna, Yasunori Endo, The 14th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2017), The 14th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2017), Sep. 2016 , Refereed
- On Cluster Validity Measures based x-means, Yukihiro Hamasuna, Yasunori Endo, The 12th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2015), The 12th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2015), Sep. 2015 , Refereed
- Non Metric Model Based on Rough Set Representation., Yasunori Endo, Ayako Heki, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), 17(4), 540 - 551, Jul. 2013 , Refereed
- Semi-supervised Fuzzy c-Means Clustering for Data with Clusterwise Tolerance with Pairwise Constraints, Yukihiro Hamasuna, Yasunori Endo, Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems (SCIS & ISIS 2010), Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems (SCIS & ISIS 2010), Dec. 2010 , Refereed
- Fuzzy c-Regression Model for Data with Tolerance, Kouta Kurihara, Yasunori Endo, Yukihiro Hamasuna, Sadaaki Miyamoto, The 6th International Conference on Modeling Decisions for Artificial Intelligence (MDAI2009), The 6th International Conference on Modeling Decisions for Artificial Intelligence (MDAI2009), Dec. 2009 , Refereed
- On Hierarchical Clustering for Data with Tolerance, Yasunori Endo, Yukihiro Hamasuna, Ayaka Tagaya, The 6th International Conference on Modeling Decisions for Artificial Intelligence (MDAI2009), The 6th International Conference on Modeling Decisions for Artificial Intelligence (MDAI2009), Dec. 2009 , Refereed
- Two types of Tolerant Hard c-Means Clustering, Yukihiro Hamasuna, Yasunori Endo, 2009 International Symposium on Nonlinear Theory and its Applications (Nolta2009), 2009 International Symposium on Nonlinear Theory and its Applications (Nolta2009), Oct. 2009 , Refereed
- On Projection Correlation Proposal for a New Dissimilarity and Application to Hierarchical Clustering Algorithms, Yasunori Endo, Fuyuki Uchida, Yukihiro Hamasuna, Modeling Decisions for Artificial Intelligence (MDAI2008), Modeling Decisions for Artificial Intelligence (MDAI2008), Oct. 2008 , Refereed
- New Clustering Algorithms by using Tolerance Vector, Yukihiro Hamasuna, Yasunori Endo, Modeling Decisions for Artificial Intelligence (MDAI2008), Modeling Decisions for Artificial Intelligence (MDAI2008), Oct. 2008 , Refereed
- On a New Dissimilarity of Projection Correlation, Yasunori Endo, Fuyuki Uchida, Yukihiro Hamasuna, Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2008), Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2008), Sep. 2008 , Refereed
- On Fuzzy c-Means for Data with Uncertainty using Spring Modulus, Yasushi Hasegawa, Yasunori Endo, Yukihiro Hamasuna, Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2008), Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems (SCIS & ISIS 2008), Sep. 2008 , Refereed
- Fuzzy c-means for Data with Rectangular Maximum Tolerance Range, Yasunori Endo, Yasushi Hasegawa, Yukihiro Hamasuna, Sadaaki Miyamoto, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), 12(5), 461 - 466, Sep. 2008 , Refereed
- 許容範囲付きデータに対するハードクラスタリング, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, Yasushi Hasegawa, Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, 20(3), 388 - 398, Jun. 2008 , Refereed
- Clustering Algorithms Based on Tolerance Vector Concept, Yasunori Endo, Yasushi Hasegawa, Yukihiro Hamasuna, Sadaaki Miyamoto, Proc. 2007 International Symposium on Nonlinear Theory and Its Applications (Nolta2007), Proc. 2007 International Symposium on Nonlinear Theory and Its Applications (Nolta2007), Sep. 2007 , Refereed
- Metaheuristic Algorithms for Container Loading Problems: Framework and Knowledge Utilization, Sadaaki Miyamoto, Yasunori Endo, Koki Hanzawa, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), 11(1), 51 - 60, Jan. 2007 , Refereed
- Metaheuristic Algorithms for Container Loading Problem by Grouping Objects, Yasunori Endo, Koki Hanzawa, Yukihiro Hamasuna, Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, 18(6), 859 - 866, Dec. 2006 , Refereed
- Metaheuristic Al- gorithms for Container Loading Problem Using Grouping Objects, Yasunori Endo, Sadaaki Miyamoto, Koki Hanzawa, Yukihiro Hamasuna, Proc. 2006 International Symposium on Nonlinear Theory and Its Applications (Nolta2006), Proc. 2006 International Symposium on Nonlinear Theory and Its Applications (Nolta2006), Sep. 2006 , Refereed
- Container Loading Problem: Formulation, Knowledge Utilization, and Algorithms, Yasunori Endo, Sadaaki Miyamoto, Koki Hanzawa, Yukihiro Hamasuna, Modeling Decisions for Artificial Intelligence (MDAI2005), Modeling Decisions for Artificial Intelligence (MDAI2005), Jul. 2005 , Refereed
- Two-stage clustering based on cluster validity measures, Yukihiro Hamasuna, Ryo Ozaki, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 22(1), 54 - 61, Jan. 01 2018 , RefereedSummary:To handle a large-scale object, a two-stage clustering method has been previously proposed. The method generates a large number of clusters during the first stage and merges clusters during the second stage. In this paper, a novel two-stage clustering method is proposed by introducing cluster validity measures as the merging criterion during the second stage. The significant cluster validity measures used to evaluate cluster partitions and determine the suitable number of clusters act as the criteria for merging clusters. The performance of the proposed method based on six typical indices is compared with eight artificial datasets. These experiments show that a trace of the fuzzy covariance matrix Wtr and its kernelization KWtr are quite effective when applying the proposed method, and obtain better results than the other indices.
- Even-sized clustering based on optimization and its variants, Yasunori Endo, Yukihiro Hamasuna, Tsubasa Hirano, Naohiko Kinoshita, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 22(1), 62 - 69, Jan. 01 2018 , RefereedSummary:A clustering method referred to as K-member clustering classifies a dataset into certain clusters, the size of which is more than a given constant K. Even-sized clustering, which classifies a dataset into even-sized clusters, is also considered along with K-member clustering. In our previous study, we proposed Even-sized Clustering Based on Optimization (ECBO) to output adequate results by formulating an even-sized clustering problem as linear programming. The simplex method is used to calculate the belongingness of each object to clusters in ECBO. In this study, ECBO is extended by introducing ideas that were introduced in Kmeans or fuzzy c-means to resolve problems of initialvalue dependence, robustness against outliers, calculation costs, and nonlinear boundaries of clusters. We also reconsider the relation between the dataset size, the cluster number, and K in ECBO. Moreover, we verify the effectiveness of the variants of ECBO based on experimental results using synthetic datasets and a benchmark dataset.
- Agglomerative hierarchical clustering based on local optimization for cluster validity measures, Ryo Ozaki, Yukihiro Hamasuna, Yasunori Endo, 2017 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2017, 2017 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2017, 2017-, 1822 - 1827, Nov. 27 2017 , RefereedSummary:Modularity is an evaluation measure for graph clustering. Louvain method is constructed by local optimization for modularity and is bottom up method as well as agglomerative hierarchical clustering. Cluster validity measures are used to evaluate cluster partitions as well as modularity. They are traditional evaluation measures in the field of clustering. We propose a novel graph clustering which is based on agglomerative hierarchical clustering. The proposed method in this study is constructed by local optimization for cluster validity measures. The effectiveness of the proposed method is shown through numerical examples. Numerical examples show that the proposed method has different clustering propety from Louvain method because of the feature of cluster validity measures.
- Hierarchical clustering algorithms with automatic estimation of the number of clusters, Ryosuke Abe, Sadaaki Miyamoto, Yasunori Endo, Yukihiro Hamasuna, IFSA-SCIS 2017 - Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems, IFSA-SCIS 2017 - Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems, 1 - 5, Aug. 30 2017 , RefereedSummary:The problem of estimating appropriate number of clusters has been a main and difficult issue in clustering researches. There are different methods for this in hierarchical clustering a typical approach is to try clustering for different number of clusters, and compare them using a measure to estimate cluster numbers. On the other hand, there is no such method to estimate automatically the number of clusters in agglomerative hierarchical clustering (AHC), since AHC produces a family of clusters with different cluster numbers at the same time using the form of dendrograms. An exception is the Newman method in network clustering, but this method does not have a useful dendrogram output. The aim of the present paper is to propose new methods to automatically estimate the number of clusters in AHC. We show two approaches for this purpose, one is to use a variation of cluster validity measure, and another is to use statistical model selection method like BIC.
- A study on cluster validity measures for clustering network data, Yukihiro Hamasuna, Ryo Ozaki, Yasunori Endo, IFSA-SCIS 2017 - Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems, IFSA-SCIS 2017 - Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems, 1 - 6, Aug. 30 2017 , RefereedSummary:Modularity is one of the evaluation measures for network data and used as the criterion of merging two clusters in Louvain method. To construct useful cluster validity measures for network data, the effectiveness of eight conventional cluster validity measures are compared with Modularity. Cluster partitions of six artificial network datasets are obtained by k-medoids and evaluated by cluster validity measures including Modularity. Numerical experiments show that the Dunn's index is effective in conventional cluster validity measures than other indices.
- On various types of controlled-sized clustering based on optimization, Yasunori Endo, Sachiko Ishida, Naohiko Kinoshita, Yukihiro Hamasuna, IEEE International Conference on Fuzzy Systems, IEEE International Conference on Fuzzy Systems, 1 - 6, Aug. 23 2017 , RefereedSummary:Clustering is one of unsupervised classification method, that is, it classifies a data set into some clusters without any external criterion. Typical clustering methods, e.g. k-means (KM) or fuzzy c-means (FCM) are constructed based on optimization of the given objective function. Many clustering methods as well as KM and FCM are formulated as optimization problems with typical objective functions and constraints. The objective function itself is also an evaluation guideline of results of clustering methods. Considered together with its theoretical extensibility, there is the great advantage to construct clustering methods in the framework of optimization. From the viewpoint of optimization, some of the authors proposed an Even-sized Clustering method Based on Optimization (ECBO), which is with tight constraints of cluster size, and constructed some variations of ECBO. The constraint considered in ECBO is that each cluster size is K or K + 1, and the belongingness of each object to clusters is calculated by the simplex method in each iteration. It is considered that ECBO has the advantage in the viewpoint of clustering accuracy, cluster size, and optimization framework than other similar methods. However, the constraint of cluster sizes of ECBO is tight in the meaning of cluster size so that it may be inconvenient in case that some extra margin of cluster size is allowed. Moreover, it is expected that new clustering algorithms in which each cluster size can be controlled deal with more various datasets. From the above view point, we proposed two new clustering algorithms based on ECBO. One is COntrolled-sized Clustering Based on Optimization (COCBO), and the other is an extended COCBO, which is referred to as COntrolled-sized Clustering Based on Optimization++ (COCBO++). Each cluster size can be controlled in the algorithms. However, these algorithms have some problems. In this paper, we will describe various types of COCBO to solve the above problems and estimate the methods in some numerical examples.
- On some clustering algorithms based on tolerance, Yukihiro Hamasuna, Yasunori Endo, Studies in Computational Intelligence, Studies in Computational Intelligence, 671, 87 - 99, Jan. 01 2017 , RefereedSummary:A large number of clustering algorithms have been proposed to handle target data and deal with various real-world problems such as uncertain data mining, semi-supervised learning and so on. We focus above two topics and introduce two concepts to construct significant clustering algorithms. We propose tolerance and penalty-vector concepts for handling uncertain data. We also propose clusterwise tolerance concept for semi-supervised learning. These concepts are quite similar approach in the viewpoint of handling objects to be flexible to each clustering topics. We construct two clustering algorithms FCMT and FCMQ for handling uncertain data. We also construct two clustering algorithms FCMCT and SSFCMCT for semi- supervised learning. We consider that those concepts have a potential to resolve conventional and brand new clustering topics in various ways.
- Comparison of cluster validity measures based x-means, Yukihiro Hamasuna, Naohiko Kinoshita, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 20(5), 845 - 853, Sep. 01 2016 , RefereedSummary:The x-means determines the suitable number of clusters automatically by executing k-means recursively. The Bayesian Information Criterion is applied to evaluate a cluster partition in the x-means. A novel type of x-means clustering is proposed by introducing cluster validity measures that are used to evaluate the cluster partition and determine the number of clusters instead of the information criterion. The proposed x- means uses cluster validity measures in the evaluation step, and an estimation of the particular probabilistic model is therefore not required. The performances of a conventional x-means and the proposed method are compared for crisp and fuzzy partitions using eight datasets. The comparison shows that the proposed method obtains better results than the conventional method, and that the cluster validity measures for a fuzzy partition are effective in the proposed method.
- On Fuzzy non-metric model for data with tolerance and its application to incomplete data clustering, Yasunori Endo, Tomoyuki Suzuki, Naohiko Kinoshita, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 20(4), 571 - 579, 2016 , RefereedSummary:The fuzzy non-metric model (FNM) is a representative non-hierarchical clustering method, which is very useful because the belongingness or the membership degree of each datum to each cluster can be calculated directly from the dissimilarities between data and the cluster centers are not used. However, the original FNM cannot handle data with uncertainty. In this study, we refer to the data with uncertainty as "uncertain data," e.g., incomplete data or data that have errors. Previously, a methods was proposed based on the concept of a tolerance vector for handling uncertain data and some clustering methods were constructed according to this concept, e.g. fuzzy c-means for data with tolerance. These methods can handle uncertain data in the framework of optimization. Thus, in the present study, we apply the concept to FNM. First, we propose a new clustering algorithm based on FNMusing the concept of tolerance, which we refer to as the fuzzy non-metric model for data with tolerance. Second, we show that the proposed algorithm can handle incomplete data sets. Third, we verify the effectiveness of the proposed algorithm based on comparisons with conventional methods for incomplete data sets in some numerical examples.
- On Various Types of Even-Sized Clustering Based on Optimization, Yasunori Endo, Tsubasa Hirano, Naohiko Kinoshita, Yikihiro Hamasuna, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, (MDAI 2016), MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, (MDAI 2016), 9880, 165 - 177, 2016 , RefereedSummary:Clustering is a very useful tool of data mining. A clustering method which is referred to as K-member clustering is to classify a dataset into some clusters of which the size is more than a given constant K. The K-member clustering is useful and it is applied to many applications. Naturally, clustering methods to classify a dataset into some even-sized clusters can be considered and some even-sized clustering methods have been proposed. However, conventional even-sized clustering methods often output inadequate results. One of the reasons is that they are not based on optimization. Therefore, we proposed Even-sized Clustering Based on Optimization (ECBO) in our previous study. The simplex method is used to calculate the belongingness of each object to clusters in ECBO. In this study, ECBO is extended by introducing some ideas which were introduced in k-means or fuzzy c-means to improve problems of initial-value dependence, robustness against outliers, calculation cost, and nonlinear boundaries of clusters. Moreover, we reconsider the relation between the dataset size, the cluster number, and K in ECBO.
- A Method of Two-Stage Clustering Based on Cluster Validity Measures, Ryo Ozaki, Yukihiro Hamasuna, Yasunori Endo, 2016 JOINT 8TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 17TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 2016 JOINT 8TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 17TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 410 - 415, 2016 , RefereedSummary:Two-stage clustering is constructed from generating stage and merging one. To handle a large scale of objects, an algorithm of the two-stage clustering generates a large number of clusters in the first stage and merge clusters in the second stage. A novel two-stage clustering method is proposed by introducing cluster validity measures which are used to evaluate cluster partition and determine the suitable number of clusters. The significant cluster validity measure is used in the second stage and play a role as criterion to merge clusters. The performance of the proposed method are compared with six artificial datasets and three benchmark datasets. These experiments show that several cluster validity measures, that is, trace of fuzzy covariance matrix and membership degrees based indices are effective in the proposed method and obtain better results than other indices.
- On Kernelized Sequential Hard Clustering, Yukihiro Hamasuna, Yasunori Endo, 2016 JOINT 8TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 17TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 2016 JOINT 8TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 17TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 416 - 419, 2016 , RefereedSummary:A method of sequential clustering extracts a cluster sequentially without determining the number of clusters. The sequential hard clustering is based on noise clustering and one of the typical sequential clustering methods. A kernelized sequential hard clustering is proposed by introducing the kernel method to sequential hard clustering to handle datasets which consists non-linear clusters and execute robust clustering. The performance of the proposed method is evaluated with a typical dataset which consists non-linear cluster boundary. Negative results are obtained through numerical examples and those show that the proposed method can not extract non-linear clusters
- Fuzzy non-metric model for data with tolerance and its application to incomplete data clustering, Yasunori Endo, Tomoyuki Suzuki, Naohiko Kinoshita, Yukihiro Hamasuna, Sadaaki Miyamoto, IEEE International Conference on Fuzzy Systems, IEEE International Conference on Fuzzy Systems, 2015-, Nov. 25 2015 , RefereedSummary:Clustering is a technique of unsupervised classification. The methods are classified into two types, one is hierarchical and the other is non-hierarchical. Fuzzy non-metric model (FNM) is a representative method of non-hierarchical clustering. FNM is very useful because belongingness or the membership degree of each datum to each cluster is calculated directly from dissimilarities between data, and cluster centers are not used. However FNM cannot handle data with uncertainty, called uncertain data, e.g. incomplete data, or data which have errors. In order to handle such data, concept of tolerance vector has been proposed. The clustering methods using the concept can handle the uncertain data in the framework of optimization, e.g. fuzzy c-means for data with tolerance (FCM-T). In this paper, we will first propose new clustering algorithm to apply the concept of tolerance to FNM, called fuzzy non-metric model for data with tolerance (FNM-T). Second, we will show that the proposed algorithm handle incomplete data sets. Third, we will verify the effectiveness of the proposed algorithm in comparison with conventional ones for incomplete data sets through some numerical examples.
- Fuzzy c-means with quadratic penalty-vector regularization using kullback-leibler information for uncertain data, Naohiko Kinoshita, Yasunori Endo, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 19(5), 624 - 631, Sep. 01 2015 , RefereedSummary:Clustering, a highly useful unsupervised classification, has been applied in many fields. When, for example, we use clustering to classify a set of objects, it generally ignores any uncertainty included in objects. This is because uncertainty is difficult to deal with and model. It is desirable, however, to handle individual objects as is so that we may classify objects more precisely. In this paper, we propose new clustering algorithms that handle objects having uncertainty by introducing penalty vectors. We show the theoretical relationship between our proposal and conventional algorithms verifying the effectiveness of our proposed algorithms through numerical examples.
- On sequential cluster extraction based on L1-regularized possibilistic c-means, Yukihiro Hamasuna, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 19(5), 655 - 661, Sep. 01 2015 , RefereedSummary:Sequential cluster extraction algorithms are useful clustering methods that extract clusters one by one without the number of clusters having to be determined in advance. Typical examples of these algorithms are sequential hard c-means (SHCM) and possibilistic clustering (PCM) based algorithms. Two types of L1-regularized possibilistic clustering are proposed to induce crisp and possibilistic allocation rules and to construct a novel sequential cluster extraction algorithm. The relationship between the proposed method and SHCM is also discussed. The effectiveness of the proposed method is verified through numerical examples. Results show that the entropy-based method yields better results for the Rand Index and the number of extracted clusters.
- Fuzzy Non-metric Model for Data with Tolerance and Its Application to Incomplete Data Clustering, Yasunori Endo, Tomoyuki Suzuki, Naohiko Kinoshita, Yukihiro Hamasuna, Sadaaki Miyamoto, 2015 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2015), 2015 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2015), 20(4), 571 - 579, 2015 , RefereedSummary:Clustering is a technique of unsupervised classification. The methods are classified into two types, one is hierarchical and the other is non-hierarchical. Fuzzy non-metric model (FNM) is a representative method of non-hierarchical clustering. FNM is very useful because belongingness or the membership degree of each datum to each cluster is calculated directly from dissimilarities between data, and cluster centers are not used. However FNM cannot handle data with uncertainty, called uncertain data, e.g. incomplete data, or data which have errors. In order to handle such data, concept of tolerance vector has been proposed. The clustering methods using the concept can handle the uncertain data in the framework of optimization, e.g. fuzzy c-means for data with tolerance (FCM-T). In this paper, we will first propose new clustering algorithm to apply the concept of tolerance to FNM, called fuzzy non-metric model for data with tolerance (FNM-T). Second, we will show that the proposed algorithm handle incomplete data sets. Third, we will verify the effectiveness of the proposed algorithm in comparison with conventional ones for incomplete data sets through some numerical examples.
- On a family of new sequential hard clustering, Yukihiro Hamasuna, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 19(6), 759 - 765, 2015 , RefereedSummary:This paper presents a new algorithm of sequential cluster extraction based on hard c-means and hard c-medoids clustering. Sequential cluster extraction means that the algorithm extracts 'one cluster at a time.' A characteristic parameter, called a noise parameter, is used in noise clustering based sequential clustering. We propose a novel sequential clustering method called new sequential clustering, extracts an arbitrary number of objects as one cluster by considering the noise parameter as a variable to be optimized. Experimental results with four data sets confirm the effectiveness of our proposal. These results also show that classification results strongly depend on parameter ν and that our proposal is applicable to the first stage in a two-stage clustering algorithm.
- Fuzzy Non-metric Model for Data with Tolerance and Its Application to Incomplete Data Clustering, Yasunori Endo, Tomoyuki Suzuki, Naohiko Kinoshita, Yukihiro Hamasuna, Sadaaki Miyamoto, 2015 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2015), 2015 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2015), 1 - 7, 2015 , RefereedSummary:Clustering is a technique of unsupervised classification. The methods are classified into two types, one is hierarchical and the other is non-hierarchical. Fuzzy non-metric model (FNM) is a representative method of non-hierarchical clustering. FNM is very useful because belongingness or the membership degree of each datum to each cluster is calculated directly from dissimilarities between data, and cluster centers are not used. However FNM cannot handle data with uncertainty, called uncertain data, e.g. incomplete data, or data which have errors. In order to handle such data, concept of tolerance vector has been proposed. The clustering methods using the concept can handle the uncertain data in the framework of optimization, e.g. fuzzy c-means for data with tolerance (FCM-T). In this paper, we will first propose new clustering algorithm to apply the concept of tolerance to FNM, called fuzzy non-metric model for data with tolerance (FNM-T). Second, we will show that the proposed algorithm handle incomplete data sets. Third, we will verify the effectiveness of the proposed algorithm in comparison with conventional ones for incomplete data sets through some numerical examples.
- On cluster extraction from relational data using L1-regularized possibilistic assignment prototype algorithm, Yukihiro Hamasuna, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 19(1), 23 - 28, Jan. 01 2015 , RefereedSummary:This paper proposes entropy-based L1-regularized possibilistic clustering and a method of sequential cluster extraction from relational data. Sequential cluster extraction means that the algorithm extracts cluster one by one. The assignment prototype algorithm is a typical clustering method for relational data. The membership degree of each object to each cluster is calculated directly from dissimilarities between objects. An entropy-based L1-regularized possibilistic assignment prototype algorithm is proposed first to induce belongingness for a membership grade. An algorithm of sequential cluster extraction based on the proposed method is constructed and the effectiveness of the proposed methods is shown through numerical examples.
- On New Sequential Hard c-Medoids, Yukihiro Hamasuna, Yasunori Endo, 2014 JOINT 7TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 15TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 2014 JOINT 7TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 15TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 489 - 494, 2014 , RefereedSummary:This paper presents a new sequential cluster extraction algorithm based on hard c-medoids clustering. The word sequential cluster extraction means that the algorithm extract one cluster at a time. The hard c-medoids is one of the variants of hard c-means clustering. The cluster medoid which is referred to as representative of each cluster is an object in hard c-medoids. The sequential clustering algorithms are based on Dave's noise clustering approach. A characteristic parameter which is called noise parameter is used in noise clustering. We construct a new sequential hard c-medoids algorithm by considering the noise parameter as a variables in optimization problem. First, the optimization problem of new sequential hard c-medoids clustering is introduced. Next, the sequential clustering algorithm is constructed based on the optimization problem. Moreover, the effectiveness of proposed method is shown through numerical experiments.
- On Even-sized Clustering Algorithm Based on Optimization, Tsubasa Hirano, Yasunori Endo, Naohiko Kinoshita, Yukihiro Hamasuna, 2014 JOINT 7TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 15TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 2014 JOINT 7TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (SCIS) AND 15TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS (ISIS), 495 - 500, 2014 , RefereedSummary:Clustering methods to divide a data set into some clusters of which the size is more than a given constant K, are very useful in many applications. The methods are called K-member clustering (KMC). As a natural result, clustering methods to divide a data set into even-sized clusters can be considered. However, there are no algorithms of such methods based on optimization. That is why the conventional algorithms often output inadequate results. Therefore we should consider an algorithm based on optimization. In this paper, we propose even-sized clustering algorithm using simplex method which is one of optimization method, and verify the proposed method through some numerical examples.
- On Cluster Extraction from Relational Data Using Entropy Based Relational Crisp Possibilistic Clustering, Yukihiro Hamasuna, Yasunori Endo, KNOWLEDGE AND SYSTEMS ENGINEERING (KSE 2013), VOL 2, KNOWLEDGE AND SYSTEMS ENGINEERING (KSE 2013), VOL 2, 245, 57 - 67, 2014 , RefereedSummary:The relational clustering is one of the clustering methods for relational data. The membership grade of each datum to each cluster is calculated directly from dissimilarities between datum and the cluster center which is referred to as representative of cluster is not used in relational clustering. This paper discusses a new possibilistic approach for relational clustering from the viewpoint of inducing the crispness. In the previous study, crisp possibilistic clustering and its variant has been proposed by using L-1-regularization. These crisp possibilistic clustering methods induce the crispness in the membership function. In this paper, entropy based crisp possibilistic relational clustering is proposed for handling relational data. Next, the way of sequential extraction is also discussed. Moreover, the effectiveness of proposed method is shown through numerical examples.
- Hard and Fuzzy c-means Algorithms with Pairwise Constraints by Non-metric Terms, Yasunori Endo, Naohiko Kinoshita, Kuniaki Iwakura, Yukihiro Hamasuna, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2014, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2014, 8825, 145 - 157, 2014 , RefereedSummary:Recently, semi-supervised clustering has been focused, e.g., Refs. [2-5]. The semi-supervised clustering algorithms improve clustering results by incorporating prior information with the unlabeled data. This paper proposes three new clustering algorithms with pairwise constraints by introducing non-metric term to objective functions of the well-known clustering algorithms. Moreover, its effectiveness is verified through some numerical examples.
- Semi-Supervised Hard and Fuzzy c-Means with Assignment Prototype Term, Yukihiro Hamasuna, Yasunori Endo, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2014, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2014, 8825, 135 - 144, 2014 , RefereedSummary:Semi-supervised learning is an important task in the field of data mining. Pairwise constraints such as must-link and cannot-link are used in order to improve clustering properties. This paper proposes a new type of semi-supervised hard and fuzzy c-means clustering with assignment prototype term. The assignment prototype term is based on the Windham's assignment prototype algorithm which handles pairwise constraints between objects in the proposed method. First, an optimization problem of the proposed method is formulated. Next, a new clustering algorithm is constructed based on the above discussions. Moreover, the effectiveness of the proposed method is shown through numerical experiments.
- On New Sequential Hard c-Means and its Kernelization, Yukihiro Hamasuna, Yasunori Endo, 2014 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING (GRC), 2014 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING (GRC), 82 - 87, 2014 , RefereedSummary:This paper presents a new sequential clustering algorithm based on sequential hard c-means clustering. The word sequential cluster extraction means that the algorithm extract one cluster at a time. The sequential hard c-means is one of the typical and conventional sequential clustering methods. The proposed new sequential clustering algorithm is based on Dave's noise clustering approach. A characteristic parameter which is called noise parameter is applied in Dave's approach. We construct a new sequential hard c-means algorithm by introducing another new parameter which controls a number of extracting objects and considering the noise parameter as a variables in optimization problem. First, the optimization problem of new sequential hard c-means clustering is introduced. Next, the sequential clustering algorithm and its kernelization are constructed based on above optimization problem. Moreover, the effectiveness of proposed method is shown through numerical experiments.
- Sequential extraction by using two types of crisp possibilistic clustering, Yukihiro Hamasuna, Yasunori Endo, Proceedings - 2013 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2013, Proceedings - 2013 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2013, 2013 Vol.5, 3505 - 3510, 2013 , RefereedSummary:Possibilistic clustering is well-known as one of the useful clustering methods because it is robust against noise or outlier in data. In the previous study, sparse possibilistic clustering and its variant has been proposed by using 1-regularization. These possibilistic clustering methods with 1-regularization are quite different from the viewpoint of membership function. Two types of new possibilistic approach with 1- regularization named crisp possibilistic clustering are proposed in this paper. Classification function of proposed methods which shows allocation rule in whole space and the way of sequential cluster extraction are also proposed. The effectiveness of proposed methods is, moreover, shown through numerical examples. © 2013 IEEE.
- On sequential cluster extraction based on L1-regularized possibilistic non-metric model, Yukihiro Hamasuna, Yasunori Endo, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8234, 204 - 213, 2013 , RefereedSummary:The fuzzy non-metric model is one of the clustering methods in which the membership grade of each datum to each cluster is calculated directly from dissimilarities between data. The cluster center which is referred to as representative of cluster is not used in fuzzy non-metric model. This paper discusses a new possibilistic approach for non-metric model from the viewpoint of being in the cluster. In the previous study, new possibilistic clustering and its variant have been proposed by using L1-regularization. These possibilistic clustering methods with L1-regularization induce a change in the membership function. Two types of non-metric model based on possibilistic approach named L1-regularized possibilistic non-metric model are proposed in this paper. Next, the way of sequential extraction algorithm is also discussed. Moreover, the results of sequential extraction based on proposed methods are shown. © 2013 Springer-Verlag.
- On semi-supervised fuzzy c-means clustering for data with clusterwise tolerance by opposite criteria, Yukihiro Hamasuna, Yasunori Endo, SOFT COMPUTING, SOFT COMPUTING, 17(1), 71 - 81, Jan. 2013 , RefereedSummary:This paper presents a new semi-supervised fuzzy c-means clustering for data with clusterwise tolerance by opposite criteria. In semi-supervised clustering, pairwise constraints, that is, must-link and cannot-link, are frequently used in order to improve clustering performances. From the viewpoint of handling pairwise constraints, a new semi-supervised fuzzy c-means clustering is proposed by introducing clusterwise tolerance-based pairwise constraints. First, a concept of clusterwise tolerance-based pairwise constraints is introduced. Second, the optimization problems of the proposed method are formulated. Especially, must-link and cannot-link are handled by opposite criteria in our proposed method. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of the proposed algorithm is verified through numerical examples.
- On Sparse Possibilistic Clustering with Crispness - Classification Function and Sequential Extraction, Yukihiro Hamasuna, Yasunori Endo, 6TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS, AND THE 13TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS, 6TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS, AND THE 13TH INTERNATIONAL SYMPOSIUM ON ADVANCED INTELLIGENT SYSTEMS, 1801 - 1806, 2012 , RefereedSummary:In addition to fuzzy c-means clustering, possibilistic clustering is well-known as one of the useful techniques because it is robust against noise in data. Especially sparse possibilistic clustering is quite different from other possibilistic clustering methods in the point of membership function. We propose a way to induce the crispness in possibilistic clustering by using L-1-regularization and show classification function of sparse possibilistic clustering with crispness for understanding allocation rule. We, moreover, show the way of sequential extraction by proposed method. After that, we show the effectiveness of the proposed method through numerical examples.
- On rough set based non metric model, Yasunori Endo, Ayako Heki, Yukihiro Hamasuna, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7647, 394 - 407, 2012 , RefereedSummary:Non metric model is a kind of clustering method in which belongingness or the membership grade of each object to each cluster is calculated directly from dissimilarities between objects and cluster centers are not used. By the way, the concept of rough set is recently focused. Conventional clustering algorithms classify a set of objects into some clusters with clear boundaries, that is, one object must belong to one cluster. However, many objects belong to more than one cluster in real world, since the boundaries of clusters overlap with each other. Fuzzy set representation of clusters makes it possible for each object to belong to more than one cluster. On the other hand, the fuzzy degree sometimes may be too descriptive for interpreting clustering results. Rough set representation could handle such cases. Clustering based on rough set representation could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering. This paper shows two type of Rough set based Non Metric model (RNM). One algorithm is Rough set based Hard Non Metric model (RHNM) and the other is Rough set based Fuzzy Non Metric model (RFNM). In the both algorithms, clusters are represented by rough sets and each cluster consists of lower and upper approximation. Second, the proposed methods are kernelized by introducing kernel functions which are a powerful tool to analize clusters with nonlinear boundaries. © 2012 Springer-Verlag.
- Hard c-means using quadratic penalty-vector regularization for uncertain data, Yasunori Endo, Arisa Taniguchi, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 16(7), 831 - 840, 2012 , RefereedSummary:Clustering is an unsupervised classification technique for data analysis. In general, each datum in real space is transformed into a point in a pattern space to apply clustering methods. Data cannot often be represented by a point, however, because of its uncertainty, e.g., measurement error margin and missing values in data. In this paper, we will introduce quadratic penalty-vector regularization to handle such uncertain data using Hard c-Means (HCM), which is one of the most typical clustering algorithms. We first propose a new clustering algorithm called hard c-means using quadratic penalty-vector regularization for uncertain data (HCMP). Second, we propose sequential extraction hard c-means using quadratic penalty-vector regularization (SHCMP) to handle datasets whose cluster number is unknown. Furthermore, we verify the effectiveness of our proposed algorithms through numerical examples.
- Comparison of semi-supervised hierarchical clustering using clusterwise tolerance, Yukihiro Hamasuna, Yasunori Endo, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 16(7), 819 - 824, 2012 , RefereedSummary:This paper presents a new semi-supervised agglomerative hierarchical clustering algorithm with the ward method using clusterwise tolerance. Semi-supervised clustering has recently been noted and studied in many research fields. Must-link and cannot-link, called pairwise constraints, are frequently used in order to improve clustering properties in semi-supervised clustering. First, clusterwise tolerance based pairwise constraints are introduced in order to handle mustlink and cannot-link constraints. Next, a new semisupervised hierarchical clustering algorithm with the ward method is constructed based on the above discussions. The effectiveness of the proposed algorithms is, moreover, verified through numerical examples.
- On agglomerative hierarchical clustering using clusterwise tolerance based pairwise constraints, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 16(1), 174 - 179, 2012 , RefereedSummary:This paper presents semi-supervised agglomerative hierarchical clustering algorithm using clusterwise tolerance based pairwise constraints. In semi-supervised clustering, pairwise constraints, that is, must-link and cannot-link, are frequently used in order to improve clustering properties. From that sense, we will propose another way named clusterwise tolerance based pairwise constraints to handle must-link and cannot-link constraints in L 2-space. In addition, we will propose semi-supervised agglomerative hierarchical clustering algorithm based on it. We will, moreover, show the ffectiveness of the proposed method through numerical examples.
- On Hard c-Means Using Quadratic Penalty-Vector Regularization for Uncertain Data, Yasunori Endo, Arisa Taniguchi, Aoi Takahashi, Yukihiro Hamasuna, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2011, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2011, 6820, 126 - +, 2011 , RefereedSummary:Clustering is one of the unsupervised classification techniques of the data analysis. Data are transformed from a real space into a pattern space to apply clustering methods. However, the data cannot be often represented by a point because of uncertainty of the data, e.g., measurement error margin and missing values in data. In this paper, we introduce quadratic penalty-vector regularization to handle such uncertain data into hard c-means (HCM) which is one of the most typical clustering algorithms. First, we propose a new clustering algorithm called hard c-means using quadratic penalty-vector regularization for uncertain data (HCMP). Second, we propose sequential extraction hard c-means using quadratic penalty-vector regularization (SHCMP) to handle datasets whose cluster number is unknown. Moreover, we verify the effectiveness of our propose algorithms through some numerical examples.
- Semi-supervised Agglomerative Hierarchical Clustering with Ward Method Using Clusterwise Tolerance, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2011, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, MDAI 2011, 6820, 103 - +, 2011 , RefereedSummary:This paper presents a new semi-supervised agglomerative hierarchical clustering algorithm with ward method using clusterwise tolerance. Recently, semi-supervised clustering has been remarked and studied in many research fields. In semi-supervised clustering, must-link and cannot-link called pairwise constraints are frequently used in order to improve clustering properties. First, a clusterwise tolerance based pairwise constraints is introduced in order to handle must-link and cannot-link constraints. Next, a new semi-supervised agglomerative hierarchical clustering algorithm with ward method is constructed based on above discussions. Moreover, the effectiveness of proposed algorithms is verified through numerical examples.
- Fuzzy c-Means Clustering with Mutual Relation Constraints Construction of Two Types of Algorithms, Yasunori Endo, Yukihiro Hamasuna, KNOWLEDGE-BASED AND INTELLIGENT INFORMATION AND ENGINEERING SYSTEMS, PT I, KNOWLEDGE-BASED AND INTELLIGENT INFORMATION AND ENGINEERING SYSTEMS, PT I, 6881, 131 - 140, 2011 , RefereedSummary:Recently, semi-supervised clustering attracts many researchers' interest. In particular, constraint-based semi-supervised clustering is focused and the constraints of must-link and cannot-link play very important role in the clustering. There are many kinds of relations as well as must-link or cannot-link and one of the most typical relations is the trade-off relation. Thus, in this paper we formulate the trade-off relation and propose a new "semi-supervised" concept called mutual relation. Moreover, we construct two types of new clustering algorithms with the mutual relation constraints based on the well-known and useful fuzzy c-means, called fuzzy c-means with the mutual relation constraints.
- Hard and fuzzy c-means clustering with mutual relation constraints, Yasunon Endo, Yukihiro Hamasuna, International Conference on Intelligent Systems Design and Applications, ISDA, International Conference on Intelligent Systems Design and Applications, ISDA, 557 - 562, 2011 , RefereedSummary:Recently, semi-supervised clustering attracts many researchers' interest. In particular, constraint-based semi-supervised clustering is focused and the constraints of must-link and cannot-link play very important role in the clustering. There are many kinds of relations as well as must-link or cannot-link and one of the most typical relations is the trade-off relation. Thus, in this paper we formulate the trade-off relation and propose a new "semi-supervised" concept called mutual relation. Moreover, we construct two types of new clustering algorithms with the mutual relation constraints based on the well-known and useful hard c-means (HCM) and fuzzy c-means (FCM), called hard c-means with the mutual relation constraints (HCMMR) and fuzzy c-means with the mutual relation constraints (FCMMR). © 2011 IEEE.
- On semi-supervised fuzzy c-means clustering with clusterwise tolerance by opposite criteria, Yukihiro Hamasuna, Yasunori Endo, Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011, Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011, 225 - 230, 2011 , RefereedSummary:The importance of semi-supervised clustering is to handle pairwise constraints as a prior knowledge. In this paper, we will propose a new semi-supervised fuzzy c-means clustering with clusterwise tolerance by opposite criteria. First, the concept of clusterwise tolerance and pairwise constraints are introduced. Second, the optimization problem of proposed method is formulated. Especially, must-link and cannot-link constraints are handled and introduced by opposite criteria in proposed method. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of proposed algorithm is verified through numerical examples. © 2011 IEEE.
- On principal component analysis for data with tolerance, Yasunori Endo, Tatsuyoshi Tsuji, Yukihiro Hamasuna, Kota Kurihara, Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011, Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011, 177 - 182, 2011 , RefereedSummary:In many cases, data are handled as intervals on the pattern space because the data generally contain the uncertainty of error, loss and so on. The concept of tolerance in this paper enables us to handle these data as a point on the pattern space. The advantage is that we can handle uncertain data in the framework of optimization without introducing any particular measures between intervals. In recent years, this concept is positively introduced into clustering methods and the effectiveness is confirmed. However, there are few applications of the concept into multivariate analysis methods except regression models in spite of its effectiveness. Therefore, we propose a new algorithm of principal component analysis for uncertain data by introducing the concept of the tolerance in this paper. Moreover, we verify the effectiveness through some numerical examples. © 2011 IEEE.
- On Mahalanobis Distance Based Fuzzy c-Means Clustering for Uncertain Data Using Penalty Vector Regularization, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ 2011), IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ 2011), 810 - 815, 2011 , RefereedSummary:This paper presents Mahalanobis distance based fuzzy c-means clustering for uncertain data using penalty vector regularization. When we handle a set of data, data contains inherent uncertainty e. g., errors, ranges or some missing value of attributes. In order to handle such uncertain data as a point in a pattern space the concept of penalty vector has been proposed. Some significant clustering algorithms based on it have been also proposed. In conventional clustering algorithms, Mahalanobis distance have been used as dissimilarity as well as squared L-2 and L-1-norm. From the viewpoint of the guideline of dissimilarity, Mahalanobis distance based fuzzy c-means clustering for uncertain data should be considered. In this paper, we introduce fuzzy c-means clustering for uncertain data using penalty vector regularization as our conventional works. Next, we propose Mahalanobis distance based one. Moreover, we show the effectiveness of proposed method through numerical examples.
- Kernelized Fuzzy c-Means Clustering for Uncertain Data using Quadratic Penalty-Vector Regularization with Explicit Mappings, Yasunori Endo, Isao Takayama, Yukihiro Hamasuna, Sadaaki Miyamoto, IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ 2011), IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ 2011), 804 - 809, 2011 , RefereedSummary:Recently, fuzzy c-means clustering with kernel functions is remarkable in the reason that these algorithms can handle datasets which consist of some clusters with nonlinear boundaries. However the algorithms have the following problems: (1) the cluster centers can not be calculated explicitly, (2) it takes long time to calculate clustering results. By the way, we have proposed the clustering algorithms using penalty-vector regularization to handle uncertain data. In this paper, we propose new clustering algorithms using quadratic penalty-vector regularization by introducing explicit mappings of kernel functions to solve the following problems. Moreover, we construct fuzzy classification functions for our proposed clustering methods.
- Fuzzy c-means clustering for data with clusterwise tolerance based on L2- and L1-regularization, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 15(1), 68 - 75, 2011 , RefereedSummary:Detecting various kinds of cluster shape is an important problem in the field of clustering. In general, it is difficult to obtain clusters with different sizes or shapes by single-objective function. From that sense, we have proposed the concept of clusterwise tolerance and constructed clustering algorithms based on it. In the field of data mining, regularization techniques are used in order to derive significant classifiers. In this paper, we propose another concept of clusterwise tolerance from the viewpoint of regularization. Moreover, we construct clustering algorithms for data with clusterwise tolerance based on L2- and L1-regularization. After that, we describe fuzzy classification functions of proposed algorithms. Finally, we show the effectiveness of proposed algorithms through numerical examples.
- Fuzzy c-means clustering for uncertain data using quadratic penalty-vector regularization, Yasunori Endo, Yasushi Hasegawa, Yukihiro Hamasuna, Yuchi Kanzawa, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 15(1), 76 - 82, 2011 Summary: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 have been represented as interval ranges for which many clustering algorithms are constructed, but the lack of guidelines in selecting available distances in individual cases has made selection difficult and raised the need for ways to calculate dissimilarity between uncertain data without introducing a nearest-neighbor or other distance. The tolerance concept we propose represents uncertain data as a point with a tolerance vector, not as an interval, while this is convenient for handling uncertain data, tolerance-vector constraints make mathematical development difficult. We attempt to remove the tolerance-vector constraints using quadratic penaltyvector regularization similar to the tolerance vector. We also propose clustering algorithms for uncertain data considering optimization and obtaining an optimal solution to handle uncertainty appropriately.
- On tolerant fuzzy c-means clustering and tolerant possibilistic clustering, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, SOFT COMPUTING, SOFT COMPUTING, 14(5), 487 - 494, Mar. 2010 , RefereedSummary:This paper presents two new types of clustering algorithms by using tolerance vector called tolerant fuzzy c-means clustering and tolerant possibilistic clustering. In the proposed algorithms, the new concept of tolerance vector plays very important role. The original concept is developed to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. Using the new concept, we can consider the influence of clusters to each data by the tolerance. First, the new concept of tolerance is introduced into optimization problems. Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions. Third, new clustering algorithms are constructed based on the optimal solutions for clustering. Finally, the effectiveness of the proposed algorithms is verified through numerical examples and its fuzzy classification function.
- Semi-supervised Agglomerative Hierarchical Clustering Using Clusterwise Tolerance Based Pairwise Constraints, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE (MDAI), MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE (MDAI), 6408, 152 - 162, 2010 , RefereedSummary:Recently, semi-supervised clustering has been remarked and discussed in many researches. In semi-supervised clustering, pairwise constraints, that is, must-link and cannot-link are frequently used in order to improve clustering results by using prior knowledges or informations. In this paper, we will propose a clusterwise tolerance based pairwise constraint. In addition, we will propose semi-supervised agglomerative hierarchical clustering algorithms with centroid method based on it. Moreover, we will show the effectiveness of proposed method through numerical examples.
- Semi-supervised fuzzy c-means clustering using clusterwise tolerance based pairwise constraints, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, Proceedings - 2010 IEEE International Conference on Granular Computing, GrC 2010, Proceedings - 2010 IEEE International Conference on Granular Computing, GrC 2010, 188 - 193, 2010 , RefereedSummary:Recently, semi-supervised clustering has been remarked and discussed in many research fields. In semisupervised clustering, prior knowledge or information are often formulated as pairwise constraints, that is, must-link and cannot-link. Such pairwise constraints are frequently used in order to improve clustering properties. In this paper, we will propose a new semi-supervised fuzzy c-means clustering by using clusterwise tolerance and pairwise constraints. First, the concept of clusterwise tolerance and pairwise constraints are introduced. Second, the optimization problem of fuzzy cmeans clustering using clusterwise tolerance based pairwise constraint is formulated. Especially, must-link constraint is considered and introduced as pairwise constraints. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of proposed algorithm is verified through numerical examples. © 2010 IEEE.
- Cluster Validity Measures for Data with Tolerance, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, 2010 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2010), 2010 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2010), 1 - 6, 2010 , RefereedSummary:Cluster validity measures are used in order to determine an appropriate number of clusters and evaluate cluster partitions obtained by clustering algorithms. When we handle a set of data, data contains inherent uncertainty e. g., errors, ranges or some missing value of attributes. The concept of tolerance has been proposed from the viewpoint of handling such uncertain data. In this paper, we introduce clustering algorithms for data with tolerance. Moreover, we propose new five measures for data with tolerance, that is, the determinants and the traces of fuzzy covariance matrices, the Xie-Beni's index, the Fukuyama-Sugeno's index, and the Davies-Bouldin's index. We compare the performance of conventional ones with their tolerance versions. We found that our proposed measures takes smaller value than conventional ones. These results indicate tolerance based clustering method is suitable for handling uncertain data.
- Hard and Fuzzy c-Regression Models for Data with Tolerance in Independent and Dependent Variables, Yasunori Endo, Kouta Kurihara, Sadaaki Miyamoto, Yukihiro Hamasuna, 2010 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2010), 2010 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE 2010), 1 - 8, 2010 , RefereedSummary:c-regression models are known as very useful tools in many fields. Since now, many trials to construct c-regression models for data with uncertainty in independent and dependent variables have been done. However, there are few c-regression models for data with uncertainty in independent variables in comparison with dependent variables now. The reason is as follows. The models are constructed using optimal solutions which is derived by solving an optimization problem "analytically". The problem for data with uncertainty in dependent variables can be easily solved but it is very difficult to solve the problem for data with uncertainty in independent variables "analytically". Therefore, most of the models for data with uncertainty in independent variables are constructed in which the solutions are calculated "numerically". By the way, we have proposed "tolerance" of a convenient tool to handle data with uncertainty [3] and applied it to some of clustering algorithms [4]-[7]. This concept of tolerance is very useful. The reason is that we can handle data with uncertainty in the framework of optimization to use the concept, without introducing some particular measure between intervals. Especially when we handle the data with missing values of its attributes in the framework of optimization like as fuzzy c-means clustering [6], this tool is effective. Besides, we think that the tolerance is also available when we consider to construct a regression model for data with uncertainty in independent and dependent variables. In this paper, we first derive the optimal solutions for c-regression models for data with uncertainty in independent and dependent variables "analytically" by using the concept of tolerance. Second, we construct hard and fuzzy c-regression models for data with tolerance in independent and dependent variables. Moreover, we estimate effectiveness of the algorithms through some numerical examples.
- Clustering algorithm based on probabilistic dissimilarity, Makito Yamashiro, Yasunori Endo, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 13(4), 429 - 433, 2009 , RefereedSummary:The clustering algorithm we propose is based on probabilistic dissimilarity, which is formed by introducing the concept of probability into conventional dissimilarity. After defining probabilistic dissimilarity, we present examples of probabilistic dissimilarity functions. After considering an objective function with probabilistic dissimilarity. Furthermore, we construct a clustering algorithm probabilistic dissimilarity based using optimal solutions maximizing the objective function. Numerical examples verify the effectiveness of our algorithm.
- On L-1-Norm based Tolerant Fuzzy c-Means Clustering, Hamasuna Yukihiro, Endo Yasunori, Miyamoto Sadaaki, 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 1125 - +, 2009 , RefereedSummary:In this paper, we will propose two types of L-1-norm based tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. One is based on the constraint for tolerance vector and the other is based on the regularization term. First, the concept of clusterwise tolerance is introduced into optimization problems. In these methods, a tolerance vector attributes not only to each data but also each cluster. First, the concept of clusterwise tolerance is introduced into optimization problems. Second, optimal solutions for these optimization problems are derived. Third, new clustering algorithms are constructed based on the explicit optimal solutions. Finally, effectiveness of proposed algorithms is verified through numerical examples.
- On Tolerant Fuzzy c-Means Clustering with L-1-Regularization, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, PROCEEDINGS OF THE JOINT 2009 INTERNATIONAL FUZZY SYSTEMS ASSOCIATION WORLD CONGRESS AND 2009 EUROPEAN SOCIETY OF FUZZY LOGIC AND TECHNOLOGY CONFERENCE, PROCEEDINGS OF THE JOINT 2009 INTERNATIONAL FUZZY SYSTEMS ASSOCIATION WORLD CONGRESS AND 2009 EUROPEAN SOCIETY OF FUZZY LOGIC AND TECHNOLOGY CONFERENCE, 1152 - 1157, 2009 , RefereedSummary:We have proposed tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. This paper presents a new type of tolerant fuzzy c-means clustering with L-1-regularization. L-1-regularization is well-known as the most successful techniques to induce sparseness. The proposed algorithm is different from the viewpoint of the sparseness for tolerance vector. In the original concept of tolerance, a tolerance vector attributes to each data. This paper develops the concept to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. First, the new concept of tolerance is introduced into optimization problems. These optimization problems are based on conventional fuzzy c-means clustering (FCM). Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions and an optimization method for L-1-regularization. Third, new clustering algorithms are constructed based on the explicit optimal solutions. Finally, the effectiveness of the proposed algorithm is verified through some numerical examples.
- Comparison of Tolerant Fuzzy c-Means Clustering with L-2- and L-1-Regularization, Hamasuna Yukihiro, Endo Yasunori, Miyamoto Sadaaki, 2009 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING ( GRC 2009), 2009 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING ( GRC 2009), 197 - +, 2009 , RefereedSummary:In this paper, we will propose two types of tolerant fuzzy c-means clustering with regularization terms. One is L-2-regularization term and the other is L-1-regularization one for tolerance vector. Introducing a concept of clusterwise tolerance, we have proposed tolerant fuzzy c-means clustering from the viewpoint of handling data more flexibly. In tolerant fuzzy c-means clustering, a constraint for tolerance vector which restricts the upper bound of tolerance vector is used. In this paper, regularization terms for tolerance vector are used instead of the constraint. First, the concept of clusterwise tolerance is introduced. Second, optimization problems for tolerant fuzzy c-means clustering with regularization term are formulated. Third, optimal solutions of these optimization problems are derived. Fourth, new clustering algorithms are constructed based on the explicit optimal solutions. Finally, effectiveness of proposed algorithms is verified through numerical examples.
- On Fuzzy c-Means Clustering for Uncertain Data Using Quadratic Regularization of Penalty Vectors, Endo Yasunori, Hamasuna Yukihiro, Kanzawa Yuchi, Miyamoto Sadaaki, 2009 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING ( GRC 2009), 2009 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING ( GRC 2009), 148 - +, 2009 , RefereedSummary: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 of hard and fuzzy c-means clusterings are the most typical technique of clustering. By the way, information on a real space is transformed to data in a pattern space and analyzed in clustering. However, the data should be often represented not by a point but by a set because of uncertainty of the data, e.g., measurement error margin, data that cannot be regarded as one point, and missing values in data. These uncertainties of data have been represented as interval range and many clustering algorithms for these interval ranges of data have been constructed. However, the guideline to select an available distance in each case has not been shown so that this selection problem is difficult. Therefore, methods to calculate the dissimilarity between such uncertain data without introducing a particular distance, e.g., nearest neighbor one and so on, have been strongly desired. From this viewpoint, we have proposed a concept of tolerance. The concept represents a uncertain data not as an interval but as a point with a tolerance vector. In this paper, we try to remove the constraint for tolerance vectors by using quadratic regularization of penalty vector which is similar to tolerance vector and propose new clustering algorithms for uncertain data through considering the optimization problems and obtaining the optimal solution, to handle such uncertainty more appropriately.
- On L-1-Norm based Tolerant Fuzzy c-Means Clustering, Hamasuna Yukihiro, Endo Yasunori, Miyamoto Sadaaki, 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 1125 - +, 2009 , RefereedSummary:In this paper, we will propose two types of L-1-norm based tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. One is based on the constraint for tolerance vector and the other is based on the regularization term. First, the concept of clusterwise tolerance is introduced into optimization problems. In these methods, a tolerance vector attributes not only to each data but also each cluster. First, the concept of clusterwise tolerance is introduced into optimization problems. Second, optimal solutions for these optimization problems are derived. Third, new clustering algorithms are constructed based on the explicit optimal solutions. Finally, effectiveness of proposed algorithms is verified through numerical examples.
- On Semi-Supervised Fuzzy c-Means Clustering, Endo Yasunori, Hamasuna Yukihiro, Yamashiro Makito, Miyamoto Sadaaki, 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 2009 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-3, 1119 - +, 2009 , RefereedSummary:We have two methods of pattern classification, one is supervised and the other is unsupervised. Unsupervised classification, which is called clustering and classifies data except external criteria, is very useful in the methods of pattern classification so that it has been applied in many fields. There are two types of clustering, one is hierarchical and the other is non-hierarchical. We often use hard c-means clustering (HCM) or fuzzy c-means blustering (FCM) as typical methods of non-hierarchical clustering. By the way, supervised classification can achieve practical classification results but can't handle a lot of data. On the other hand unsupervised classification can handle a lot of data but the method is complex and sometimes results look a bit of strange. Therefore recently, study of semi-supervised classification has been studied. This classification has advantages of both of the above-mentioned methods, e.g., practical results, low costs and short calculation time. In this paper, we propose new semi-supervised classification algorithms based on fuzzy c-means clustering in which some membership grades are given as supervised membership grade in advance.
- On Tolerant Fuzzy c-Means Clustering with L-1-Regularization, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, PROCEEDINGS OF THE JOINT 2009 INTERNATIONAL FUZZY SYSTEMS ASSOCIATION WORLD CONGRESS AND 2009 EUROPEAN SOCIETY OF FUZZY LOGIC AND TECHNOLOGY CONFERENCE, PROCEEDINGS OF THE JOINT 2009 INTERNATIONAL FUZZY SYSTEMS ASSOCIATION WORLD CONGRESS AND 2009 EUROPEAN SOCIETY OF FUZZY LOGIC AND TECHNOLOGY CONFERENCE, 1152 - 1157, 2009 , RefereedSummary:We have proposed tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. This paper presents a new type of tolerant fuzzy c-means clustering with L-1-regularization. L-1-regularization is well-known as the most successful techniques to induce sparseness. The proposed algorithm is different from the viewpoint of the sparseness for tolerance vector. In the original concept of tolerance, a tolerance vector attributes to each data. This paper develops the concept to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. First, the new concept of tolerance is introduced into optimization problems. These optimization problems are based on conventional fuzzy c-means clustering (FCM). Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions and an optimization method for L-1-regularization. Third, new clustering algorithms are constructed based on the explicit optimal solutions. Finally, the effectiveness of the proposed algorithm is verified through some numerical examples.
- Clustering algorithm based on probabilistic dissimilarity, Makito Yamashiro, Yasunori Endo, Yukihiro Hamasuna, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 13(4), 429 - 433, 2009 , RefereedSummary:The clustering algorithm we propose is based on probabilistic dissimilarity, which is formed by introducing the concept of probability into conventional dissimilarity. After defining probabilistic dissimilarity, we present examples of probabilistic dissimilarity functions. After considering an objective function with probabilistic dissimilarity. Furthermore, we construct a clustering algorithm probabilistic dissimilarity based using optimal solutions maximizing the objective function. Numerical examples verify the effectiveness of our algorithm.
- On tolerant fuzzy c-means clustering, Yukihiro Hamasuna, Yasunori Endo, Sadaaki Miyamoto, Journal of Advanced Computational Intelligence and Intelligent Informatics, Journal of Advanced Computational Intelligence and Intelligent Informatics, 13(4), 421 - 428, 2009 , RefereedSummary:This paper presents a new type of clustering algorithms by using a tolerance vector called tolerant fuzzy c-means clustering (TFCM). In the proposed algorithms, the new concept of tolerance vector plays very important role. In the original concept of tolerance, a tolerance vector attributes to each data. This concept is developed to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. Using the new concept, we can consider the influence of clusters to each data by the tolerance. First, the new concept of tolerance is introduced into optimization problems based on conventional fuzzy c-means clustering (FCM). Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions. Third, new clustering algorithms are constructed based on the explicit optimal solutions of the optimization problems. Finally, the effectiveness of the proposed algorithms is verified through numerical examples by fuzzy classification function.
- On Tolerant Entropy Regularized Fuzzy c-Means, Yukihiro Hamasuna, Yasunori Endo, Makito Yamashiro, 2008 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, VOLS 1 AND 2, 2008 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, VOLS 1 AND 2, 244 - 247, 2008 , RefereedSummary:This paper presents a new type of clustering algorithm by using tolerance vector The tolerance vector is considered from a new viewpoint that the vector shows a correlation between each data and cluster centers in proposed algorithm. First, a new concept of tolerance is introduced into optimization problem. This optimization problem is based on entropy regularized fuzzy c-means. Second, the optimization problem with the tolerance is solved by using the Karush-Kuhn-Tucker conditions. Next, new clustering algorithm is constructed based on the unique and explicit optimal solutions of the optimization problem. Finally, the effectiveness of the proposed algorithm is verified through some numerical examples.
- On Tolerant Entropy Regularized Fuzzy c-Means, Yukihiro Hamasuna, Yasunori Endo, Makito Yamashiro, 2008 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, VOLS 1 AND 2, 2008 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, VOLS 1 AND 2, 244 - 247, 2008 , RefereedSummary:This paper presents a new type of clustering algorithm by using tolerance vector The tolerance vector is considered from a new viewpoint that the vector shows a correlation between each data and cluster centers in proposed algorithm. First, a new concept of tolerance is introduced into optimization problem. This optimization problem is based on entropy regularized fuzzy c-means. Second, the optimization problem with the tolerance is solved by using the Karush-Kuhn-Tucker conditions. Next, new clustering algorithm is constructed based on the unique and explicit optimal solutions of the optimization problem. Finally, the effectiveness of the proposed algorithm is verified through some numerical examples.
- Support Vector Machine for Data with Tolerance based on Hard-Margin and Soft-Margin, Hamasuna Yukihiro, Endo Yasunori, Miyamoto Sadaaki, 2008 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-5, 2008 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-5, 750 - +, 2008 , RefereedSummary:This paper presents two new types of Support Vector Machine (SVM) algorithms, one is based on Hard-margin SVM and the other is based on Soft-margin SVM. These algorithms can handle data with tolerance of which the concept includes some errors, ranges or missing values in data. First, the concept of tolerance is introduced into optimization problems of Support Vector Machine. Second, the optimization problems with the tolerance are solved by using the Karush-Kuhn-Tucker conditions. Next, new algorithms are constructed based on the unique and explicit optimal solutions of the optimization problem. Finally, the effectiveness of the proposed algorithms is verified through some numerical examples for the artificial data.
- Fuzzy c-means for data with tolerance defined as Hyper-Rectangle, Yasushi Hasegawa, Yasunori Endo, Yukihiro Hamasuna, Sadaaki Miyamoto, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, PROCEEDINGS, MODELING DECISIONS FOR ARTIFICIAL INTELLIGENCE, PROCEEDINGS, 4617, 237 - +, 2007 , RefereedSummary:The paper presents some new clustering algorithms which are based on fuzzy c-means. The algorithms can treat data with tolerance defined as hyper-rectangle. First, the tolerance is introduced into optimization problems of clustering. This is generalization of calculation errors or missing values. Next, the problems are solved and some algorithms are constructed based on the results. Finally, usefulness of the proposed algorithms are verified through numerical examples.
- Agglomerative hierarchical clustering for data with tolerance, Endo Yasunori, Hamasuna Yukihiro, Miyamoto Sadaaki, GRC: 2007 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, PROCEEDINGS, GRC: 2007 IEEE INTERNATIONAL CONFERENCE ON GRANULAR COMPUTING, PROCEEDINGS, 404 - 409, 2007 , RefereedSummary:This paper presents new clustering algorithms which are based on agglomerative hierarchical clustering (AHC) with centroid method. The algorithms can handle with data with tolerance of which the concept includes some errors, ranges, or missing values in data. First, the tolerance is introduced into optimization problems of clustering. Second, an objective function is introduced for calculating the centroid of cluster and the problem is solved using Kuhn-Tucker conditions. Next, new algorithms are constructed based on the solution of the problem. Finally, the effectiveness of the proposed algorithms in this paper is verified through some numeric examples for the artificial data.
- Two clustering algorithms for data with tolerance based on hard c-means, Yukihiro Hamasuna, Yasunori Endo, Yasushi Hasegawa, Sadaaki Miyamoto, 2007 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-4, 2007 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-4, 687 - +, 2007 , RefereedSummary:Two clustering algorithms that handle data with tolerance are proposed. One is based on hard c-means while the other uses the learning vector quantization. The concept of the tolerance includes. First, the concept of tolerance which implies errors, ranges and the loss of attribute of data is described. Optimization problems that take the tolerance into account are formulated. Since the Kuhn-Tucker condition give a unique and explicit optimal solution, an alternate minimization algorithm and a learning algorithm are constructed. Moreover, the effectiveness of the proposed algorithms is verified through numerical examples.

- A Study on Outlier Detection for Network Data by Using Fuzzy Clustering, Hamasuna Yukihiro, Ozaki Ryo, Proceedings of the Japan Joint Automatic Control Conference, 60, 0, 2017 11 , http://ci.nii.ac.jp/naid/130006251261
- Cluster Validity Measures Based Agglomerative Hierarchical Clustering for Network Data, 尾﨑 稜, 濵砂 幸裕, ファジィシステムシンポジウム講演論文集, 33, 435, 440, 2017 09 13 , http://ci.nii.ac.jp/naid/40021612498
- Clustering and others : beyond the k-means, 濵砂 幸裕, システム制御情報学会研究発表講演会講演論文集, 61, 2017 05 23 , http://ci.nii.ac.jp/naid/40021219538
- On Cluster Validity Measures Based x-means for Fuzzy Partition, Hamasuna Yukihiro, Endo Yasunori, Proceedings of the Fuzzy System Symposium, 2015 09 , http://ci.nii.ac.jp/naid/130005488329Summary:The x-means divides a set of objects without determining the number of clusters by using iterative k-means and evaluation criteria.A series of cluster validity measures is also used in order to evaluate the clustering results and determine suitable number of clusters. We propose cluster validity measures based x-means by introducing cluster validity measures instead of information criteria.We moreover show the effectiveness of the proposed methodthrough numerical examples.
- On Semi-supervised Clustering with Assignment Prototype Term, Hamasuna Yukihiro, Endo Yasunori, Proceedings of the Fuzzy System Symposium, 2014 09 , http://ci.nii.ac.jp/naid/130005480516Summary:This paper proposes a new type of semi-supervised fuzzy c -means clustering with assignment prototype term. The assignment prototype term is based on the Windham's assignment prototype algorithm which handles pairwise constraints between objects in the proposed method. First, an optimization problem of the proposed method is formulated. Next, a new clustering algorithm is constructed based on the above discussions. Moreover, the effectiveness of the proposed method is shown through numerical experiments.
- On Entropy Based Fuzzy Non-Metric Model with A Variable Controlling Cluster Sizes, Hamasuna Yukihiro, Endo Yasunori, Proceedings of the Fuzzy System Symposium, 2013 09 , http://ci.nii.ac.jp/naid/130005480371Summary:The fuzzy non-metric model is one of the clustering methods in which the membership grade of each datum to each cluster is calculated directly from dissimilarities between data. In conventional fuzzy c-means clustering, a variables for controlling cluster sizes are introduced for handling a set of data which has different sizes of clusters. We propose entropy based fuzzy non-metric model with a variable controlling cluster sizes and construct its algorithm in this paper.
- On Sparse Possibilistic Clustering with Crispness, Yukihiro Hamasuna, Yasunori Endo, Proceedings of the Fuzzy System Symposium, 28, 0, 859, 862, 2012 09 , http://ci.nii.ac.jp/naid/130005456269Summary:In addition to fuzzy $c$-means clustering, possibilistic clustering is well-known as one of the useful techniques because it is robust against noise in data. Especially sparse possibilistic clustering is quite different from other possibilistic clustering methods in the point of membership function. We propose a way to induce the crispness in possibilistic clustering by using $L_1$-regularization and show classification function of sparse possibilistic clustering with crispness for understanding allocation rule. We, moreover, show the way of sequential extraction by proposed method. After that, we show the effectiveness of the proposed method through numerical examples.
- On Semi-supervised Fuzzy c-Means Clustering Using Clusterwise Tolerance, 濵砂 幸裕, 遠藤 靖典, ファジィシステムシンポジウム講演論文集, 27, 323, 326, 2011 09 12 , http://ci.nii.ac.jp/naid/40019530566
- On Support Vector Machine for Uncertain Data with Penalty Vectors, 髙山 勲, 遠藤 靖典, 濵砂 幸裕, ファジィシステムシンポジウム講演論文集, 27, 327, 330, 2011 09 12 , http://ci.nii.ac.jp/naid/40019530577
- A Study on Cluster Validity Measures for Data with Tolerance, 日置 彩子, 遠藤 靖典, 濵砂 幸裕, ファジィシステムシンポジウム講演論文集, 27, 317, 322, 2011 09 12 , http://ci.nii.ac.jp/naid/40019530554
- On principal component analysis for data with tolerance, Yasunori Endo, Tatsuyoshi Tsuji, Yukihiro Hamasuna, Kota Kurihara, Proceedings - 2011 IEEE International Conference on Granular Computing, GrC 2011, 27, 177, 182, 2011 , 10.1109/GRC.2011.6122589, http://ci.nii.ac.jp/naid/40019530589Summary:In many cases, data are handled as intervals on the pattern space because the data generally contain the uncertainty of error, loss and so on. The concept of tolerance in this paper enables us to handle these data as a point on the pattern space. The advantage is that we can handle uncertain data in the framework of optimization without introducing any particular measures between intervals. In recent years, this concept is positively introduced into clustering methods and the effectiveness is confirmed. However, there are few applications of the concept into multivariate analysis methods except regression models in spite of its effectiveness. Therefore, we propose a new algorithm of principal component analysis for uncertain data by introducing the concept of the tolerance in this paper. Moreover, we verify the effectiveness through some numerical examples. © 2011 IEEE.