Fuzzy c-Means for Data with Rectangular Maximum Tolerance Range
Yasunori Endo*, Yasushi Hasegawa**, Yukihiro Hamasuna**, and Sadaaki Miyamoto*
*Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba
**Graduate School of Systems and Information Engineering, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
This paper provides new clustering algorithms for data with tolerance. Tolerance is understood in a broad sense, e.g., calculation errors and loss of attribute of data. The concept of tolerance is modified by using new concept of tolerance vector. First, the concept is explained and optimization problems of clustering are formulated using the vectors. Second, the problems are solved using Karush-Kuhn-Tucker conditions. Third, the new clustering algorithms are constructed by using the solutions of the problems. Moreover, the effectiveness of proposed algorithms is verified through some numerical examples.
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