Visualization of Non-Euclidean Relational Data by Robust Linear Fuzzy Clustering Based on FCMdd Framework
Katsuhiro Honda, Takeshi Yamamoto, Akira Notsu,
and Hidetomo Ichihashi
Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
Visualization is a fundamental approach for revealing intrinsic structures in multidimensional observation. This paper considers visualization of non-Euclidean relational data by extracting local linear substructures. In order to extract robust linear clusters, an FCMdd-based linear fuzzy clustering model is applied in conjunction with a robust measure of alternative c-means. Non-Euclidean data matrices are handled with β-spread transformation in a manner similar to that of NERF c-Means. In several experiments, robust feature maps derived by the robust clustering model are compared with feature maps given by the conventional clustering model and Multi-Dimensional Scaling (MDS).
and Hidetomo Ichihashi, “Visualization of Non-Euclidean Relational Data by Robust Linear Fuzzy Clustering Based on FCMdd Framework,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.2, pp. 312-317, 2013.
-  R. J. Hathaway, J. W. Davenport, and J. C. Bezdek, “Relational duals of the c-means clustering algorithms,” Pattern Recognition, Vol.22, No.2, pp. 205-212, 1989.
-  R. J. Hathaway and J. C. Bezdek, “Nerf c-means: non-Euclidean relational fuzzy clustering,” Pattern Recognition, Vol.27, No.3, pp. 429-437, 1994.
-  J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
-  R. Krishnapuram, A. Joshi, O. Nasraoui, and L. Yi, “Lowcomplexity fuzzy relational clustering algorithms for web mining,” IEEE Trans. Fuzzy Systems, Vol.9, No.4, pp. 595-607, 2001.
-  J. C. Bezdek, C. Coray, R. Gunderson, and J. Watson, “Detection and characterization of cluster substructure I. Linear structure fuzzy c-lines,” SIAM J. of Appl. Math., Vol.40, No.2, pp. 339-357, 1981.
-  J. C. Bezdek, C. Coray, R. Gunderson, and J. Watson, “Detection and characterization of cluster substructure 2. Fuzzy c-Varieties and convex combinations thereof,” SIAM J. of Appl. Math., Vol.40, No.2, pp. 358-372, 1981.
-  K. Honda and H. Ichihashi, “Linear fuzzy clustering techniques with missing values and their application to local principal component analysis,” IEEE Trans. Fuzzy Systems, Vol.12, No.2, pp. 183-193, 2004.
-  K. Honda and H. Ichihashi, “Regularized linear fuzzy clustering and probabilistic PCA mixture models,” IEEE Trans. Fuzzy Systems, Vol.13, No.4, pp. 508-516, 2005.
-  N. Haga, K. Honda, A. Notsu, and H. Ichihashi, “Local sub-space learning by extended fuzzy c-medoids clustering,” Int. J. of Knowledge Engineering and Soft Data Paradigms, Vol.2, No.2, pp. 169-181, 2010.
-  T. Yamamoto, K. Honda, A. Notsu, and H. Ichihashi, “Non-Euclidean extension of FCMdd-based linear clustering for relational data,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.8, pp. 1050-1056, 2011.
-  K.-L. Wu and M.-S. Yang, “Alternative c-means clustering algorithms,” Pattern Recognition, Vol.35, pp. 2267-2278, 2002.
-  T. Yamamoto, K. Honda, A. Notsu, and H. Ichihashi, “Robust extension of FCMdd-based linear clustering for relational data using alternative c-means criterion,” Int. J. of Computer Science and Network Security, Vol.12, No.1, pp. 47-52, 2012.
-  R. N. Davé and R. Krishnapuram, “Robust clustering methods: a unified view,” IEEE Trans. on Fuzzy Systems, Vol.5, pp. 270-293, 1997.
-  K. Honda, S. Nakao, A. Notsu, and H. Ichihashi, “Alternative fuzzy c-lines and local principal component extraction,” Int. J. of Knowledge Engineering and Soft Data Paradigms, Vol.3, No.2, pp. 188-200, 2011.
-  P.W. Holland and R. E.Welsch, “Robust regression using iteratively reweighted least-squares,” Communications in Statistics, Vol.A6, No.9, pp. 813-827, 1977.
-  W. S. Torgerson, “Theory & Methods of Scaling,” Wiley, 1958.
-  E. Z. Rothkopf, “A measure of stimulus similarity and errors in some paired-associate learning tasks,” J. Experimental Psychology, Vol.53, pp. 94-101, 1957.
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