On Objective-Based Rough c-Regression
Akira Sugawara*, Yasunori Endo**, and Naohiko Kinoshita*
*Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
**Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
The pattern recognition method of clustering is a technique automatically classifying data into clusters. Among clustering methods, c-regression based on fuzzy set theory, called Fuzzy c-Regression (FCR), is proposed to get a linear dataset structure. The most recent clustering is based on rough set theory called rough clustering, which is less descriptive than fuzzy clustering. A typical rough clustering algorithm is Rough k-Regression (RKR). However, RKR has problems because it depends on initial values and has no optimum index, so we do not know whether a clustering result will be optimal. This paper proposes Rough c-Regression (RCR) based on the optimization of an objective function and demonstrates its effectiveness through numerical examples.
-  S. Miyamoto, “Introduction to Cluster analysis,” morikita-shuppan, 1999.
-  S. Hirano and S. Tsumoto, “Rough Clustering and Its Application to Time-series Medical Data Analysis,” The 19th Annual Conf. of the Japanese Society Symp., pp. 260-265, 2007.
-  G. Peters, “Some refinements of rough k-means clustering,” Pattern Recognition, Vol.39, pp. 1481-1491, 2006.
-  Y. Endo and N. Kinoshita, “Objective-Based Rough c-Means Clustering,” Int. J. of Intelligent Systems, Vol.28, Issue 9, pp. 907-925, 2013.
-  R. J. Hathaway and J. C. Bezdek, “Switching regression models and fuzzy clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, No.3, pp. 195-204, 1993.
-  G. Peters, “Rough Clustering and Regression Analysis,” RSKT2007, LNAI 4481, pp. 292-299, 2007.
-  Z. Pawlak, “Rough sets,” Int. J. pf Computer and Information Sciences, Vol.11, No.5, pp. 341-356, 1982.
-  M. Inuiguchi, “Analysis of Information Table by Rough Set Theory,” Institute of Systems, Control and Information Engineers, Vol.49, No.5, pp. 165-172, 2005.
-  Y. Nalayama and S.Miyamoto, “Least Square Deviations and Least Absolute Deviations in c-Regression Models,” J. of of the Fuzzy System Symp., Vol.17, pp. 583-586, 2001.
-  S. Miyamoto, K. Umayahara, T. Nemoto, and O. Takata, “Algorithm of Fuzzy c-Regression Based on Least Absolute Deviations,” J. of Japan Society for Fuzzy Theory and Intelligent Informatics, Vol.12, No.4, pp. 578-587, 2000.
-  P. Lingras and G. Peters, “Rough clustering,” WIREs Data Mining and Knowledge Discovery, Vol.1, Issue.1, pp. 64-72, 2011.
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