Non Metric Model Based on Rough Set Representation
Yasunori Endo*, Ayako Heki**, and Yukihiro Hamasuna***
*Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
**Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
***Department of Informatics, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan
-  J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum, New York, 1981.
-  J. C. Bezdek, J. Keller, R. Krisnapuram, and N. R. Pal, “Fuzzy Models and Algorithms for Pattern Recognition and Image Processing,” The Handbooks of Fuzzy Sets Series, 1999.
-  M. Roubens, “Pattern classification problems and fuzzy sets,” Fuzzy Sets and Systems, Vol.1, pp. 239-253, 1978.
-  J. C. Bezdek, J. W. Davenport, and R. J. Hathaway, “Clustering with the Relational c-Means Algorithms using Different Measures of Pairwise Distance,” Proc. of the 1988 SPIE Technical Symposium on Optics, Electro-Optics, and Sensors, Vol.938, R. D. Juday (Ed.), pp. 330-337, 1988.
-  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.
-  Y. Endo, “On Entropy Based Fuzzy Non Metric Model – Proposal, Kernelization and Pairwise Constraints –,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.16, No.1, pp. 169-173, 2012.
-  P. Lingras and G. Peters, “Rough clustering,” Proc. of the 17th Int. Conf. on Machine Learning (ICML 2000), pp. 1207-1216, 2011.
-  Z. Pawlak, “Rough Sets,” Int. J. of Computer and Information Sciences, Vol.11, No.5, pp. 341-356, 1982.
-  M. Inuiguchi, “Generalizations of Rough Sets: From Crisp to Fuzzy Cases,” Proc. of Rough Sets and Current Trends in Computing, pp. 26-37, 2004.
-  Z. Pawlak, “Rough Classification,” Int. J. of Man-Machine Studies, Vol.20, pp. 469-483, 1984.
-  S. Hirano and S. Tsumoto, “An Indiscernibility-Based Clustering Method with Iterative Refinement of Equivalence Relations,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.2, pp. 169-177, 2003.
-  P. Lingras and C. West, “Interval Set Clustering of Web Users with Rough K-Means,” J. of Intelligent Information Systems, Vol.23, No.1, pp. 5-16, 2004.
-  S. Mitra, H. Banka, and W. Pedrycz, “Rough-Fuzzy Collaborative Clustering,” IEEE Trans. on Systems Man, and Cybernetics, Part B, Cybernetics, Vol.36, No.5, pp. 795-805, 2006.
-  P. Maji and S. K. Pal, “Rough Set Based Generalized Fuzzy CMeans Algorithm and Quantitative Indices,” IEEE Trans. on System, Man and Cybernetics, Part B, Cybernetics, Vol.37, No.6, pp. 1529-1540, 2007.
-  G. Peters, “Rough Clustering and Regression Analysis,” Proc. RSKT’07, LNAI 2007, Vol.4481, pp. 292-299, 2007.
-  S. Mitra and B. Barman, “Rough-Fuzzy Clustering: An Application to Medical Imagery,” Rough Set and Knowledge Technology, LNCS 2008, Vol.5009, pp. 300-307, 2008.
-  S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a Regularization and Maximum Entropy Approach,” Proc. of the 7th Int. Fuzzy Systems Association World Congress (IFSA’97), Vol.2, pp. 86-92, 1997.
-  S. Miyamoto, K. Umayahara, and M. Mukaidono, “Fuzzy Classification Functions in the Methods of Fuzzy c-Means and Regularization by Entropy,” J. of Japan Society for Fuzzy Theory and Systems Vol.10, No.3, pp. 548-557, 1998.
-  V. N. Vapnik, “Statistical Learning Theory,” Wiley, New York, 1998.
-  V. N. Vapnik, “The nature of Statistical Learning Theory,” 2nd ed., Springer, New York, 2000.
-  Y. Endo, H. Haruyama, and T. Okubo, “On Some Hierarchical Clustering Algorithms Using Kernel Functions,” IEEE Int. Conf. on Fuzzy Systems, #1106, 2004.
-  R. J. Hathaway, J. M. Huband, and J. C. Bezdek, “A Kernelized Non-Euclidean Relational Fuzzy c-Means Algorithm,” Neural, Parallel and Scientific computation, Vol.13, pp. 305-326, 2005.
-  S. Miyamoto, Y. Kawasaki, and K. Sawazaki, “An Explicit Mapping for Fuzzy c-Means Using Kernel Function and Application to Text Analysis,” IFSA/EUSFLAT 2009, 2009.
-  K. Wagstaff and C. Cardie, “Clustering with Instance-level Constraints,” Proc. of the 17th Int. Conf. on Machine Learning, pp. 1103-1110, 2000.
-  K. Wagstaff, C. Cardie, S. Rogers, and S. Schroedl, “Constrained k-means clustering with background knowledge,” Proc. of the 18th Int. Conf. on Machine Learning, pp. 577-584, 2001.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.