Semi-Supervised Fuzzy c-Means Algorithm by Revising Dissimilarity Between Data
Yuchi Kanzawa*, Yasunori Endo**, and Sadaaki Miyamoto**
*Shibaura Institute of Technology, 3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan
**University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
We propose two approaches for semi-supervised FCM with soft pairwise constraints. One applies NERFCM to the revised dissimilarity matrix by pairwise constraints. The other applies K-FCM with a dissimilarity-based kernel function, revising the dissimilarity matrix based on whether data in the same cluster may be close to each other or the data in the different clusters may be apart from each other. Propagating given pairwise constraints to unconstrained data is done when given constraints are not sufficient to obtain the desired clustering result. Numerical examples show that the proposed algorithms are valid.
-  J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum, New York, 1981.
-  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, pp. 429-437, 1994.
-  S. Miyamoto and D. Suizu, “Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines,” J. Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.1, pp. 25-30, 2003.
-  A. Bouchachia and W. Pedrycz, “Data Clustering with Partial Supervision,” Data Mining and Knowledge Discovery, Vol.12, pp. 47-78, 2006.
-  M. Yamazaki, S. Miyamoto, and I.-J. Lee, “Semi-supervised Clustering with Two Types of Additional Functions,” Proc. 24th Fuzzy System Symposium, Vol.2E2-01, 2009.
-  M. Yamashiro, Y. Endo, Y. Hamasuna, and S. Miyamoto, “A Study on Semi-supervised Fuzzy c-Means,” Proc. 24th Fuzzy System Symposium, 2E3-04, 2009.
-  Y. Kanzawa, Y. Endo, and S. Miyamoto, “A Semi-Supervised Entropy Regularized Fuzzy c-Means,” Proc. 2009 Int. Symposium on Nonlinear Theory and Its Applications, 2009.
-  K.Wagstaff, C. Cardie, S. Rogers, and S. Schroedl, “Constrained Kmeans Clustering with Background Knowledge,” Proc. Eighteenth Int. Conf. on Machine-Learning, pp. 577-584, 2001.
-  N. Grira, M. Crucianu, and N. Boujemaa, “Semi-supervised Image Database Categorization using Pairwise Constraints,” Proc. 2005 IEEE Int. Conf. on Image Processing, Vol.3, pp. 1228-1231, 2005.
-  Y. Kanzawa, Y. Endo, and S. Miyamoto, “Some Pairwise Constrained Semi-Supervised Fuzzy c-Means Clustering,” LNAI 5681, pp. 268-281, 2009.
-  Y. Kanzawa, Y. Endo, and S. Miyamoto, “Indefinite Kernel Fuzzy c-Means,” Proc. 20th Soft Science Workshop, 2010.