Fuzzy Clustering Based on Total Uncertainty Degree
Tomohito Esaki*, Tomonori Hashiyama**,
and Yahachiro Tsukamoto***
*The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Japan
**Grad. School of Information Systems, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Japan
***Dept. of Information Engineering, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tempaku-ku, Nagoya 468-8502, Japan
Traditional Fuzzy c-Means (FCM) methods have probabilistic and additive restrictions that ∑ μ (x) = 1; the sum of membership values on the identified membership function is one. Possibilistic clustering methods identify membership functions without such constraints, but some parameters used in objective functions are difficult to understand and membership function shapes are independent of clusters estimated through possibilistic methods. We propose novel fuzzy clustering using a total uncertainty degree based on evidential theory with which we obtain nonadditive membership functions whose their shapes depend on data distribution, i.e., they mutually differ. Cluster meanings thus become easier to understand than in possibilistic methods and our proposal requires only one parameter “fuzzifier.” Numerical experiments demonstrated the feasibility of our proposal conducted.
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