A new approach to fuzzification of memberships in cluster analysis

Authors:
Katsuhiro Honda;Hidetomo Ichihashi
Affiliations:
Graduate School of Engineering, Osaka Prefecture University, Osaka, Japan;Graduate School of Engineering, Osaka Prefecture University, Osaka, Japan
Venue:
MDAI'05 Proceedings of the Second international conference on Modeling Decisions for Artificial Intelligence
Year:
2005

Citing 3
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Abstract

Fuzzy c-Means (FCM) is the fuzzy version of the c-Means clustering, in which memberships are fuzzified by introducing an additional parameter into the linear objective function of weighted sum of distances between data points and cluster centers. Regularization of hard c-Means clustering is another approach to fuzzification and several regularization terms such as entropy and quadratic terms have been adopted. This paper generalizes the concept of fuzzification and proposes a new approach to fuzzy clustering. In the proposed approach, the linear weights of the hard c-Means clustering are replaced with non-linear ones by using regularization techniques. The numerical experiments demonstrate that the clustering algorithm has the features of both of the standard FCM algorithm and the regularization approaches.