Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data
Takeshi Yamamoto, Katsuhiro Honda, Akira Notsu,
and Hidetomo Ichihashi
Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, Japan
Relational data is common in many real-world applications. Linear fuzzy clustering models have been extended for handling relational data based on Fuzzy c-Medoids (FCMdd) framework. In this paper, with the goal being to handle non-Euclidean data, β-spread transformation of relational data matrices used in Non-Euclidean-type Relational Fuzzy (NERF) c-means is applied before FCMdd-type linear cluster extraction. β-spread transformation modifies data elements to avoid negative values for clustering criteria of distances between objects and linear prototypes. In numerical experiments, typical features of the proposed approach are demonstrated not only using artificially generated data but also in a document classification task with a document-keyword co-occurrence relation.
-  R. J. Hathaway, J. W. Davenport, and J. C. Bezdek, “Relational duals of the c-means clustering algorithms,” PatternRecognition, Vol.22, No.2, pp. 205-212, 1989.
-  J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
-  J. B. MacQueen, “Some methods of classification and analysis of multivariate observations,” Proc. of 5th Berkeley Symp. on Math. Stat. and Prob., pp. 281-297, 1967.
-  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.
-  L. Kaufman and P. J. Rousseeuw, “Finding Groups In Data: An Introduction To Cluster Analysis,” Wiley-Interscience, 1990.
-  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. Appl. Math., Vol.40, No.2, pp. 358-372, 1981.
-  Y. Yabuuchi and J. Watada, “Fuzzy principal component analysis and its application,” Biomedical Fuzzy and Human Sciences, Vol.3, pp. 83-92, 1997.
-  N. Kambhatla and T. K. Leen, “Dimension reduction by local principal component analysis,” Neural Computation, Vol.9, No.7, pp. 1493-1516, 1997.
-  G. E. Hinton, P. Dayan, and M. Revow, “Modeling the manifolds of images of handwritten digits,” IEEE Trans. on Neural Networks, Vol.8, No.1, pp. 65-74, 1997.
-  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.
-  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.
-  K. Honda, T. Yamamoto, N. Haga, A. Notsu, and H. Ichihashi, “Linear fuzzy cluster extraction from non-Euclidean relational data,” Proc. 2010 World Automation Congress, 2010.
-  H. Wada, K. Honda, A. Notsu, and H. Ichihashi, “Document Map Construction and Keyword Selection Based on Local PCA,” Proc. of Joint 4th Int. Conf. on Soft Computing and Intelligent Systems and 9th Int. Symp. on Advanced Intelligent Systems, pp. 682-685, 2008.
-  M. R. Anderberg, “Cluster Analysis for Applications,” Academic Press, 1973.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.