Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:B3L-F
Session:
Number:B3L-F3
Fuzzy c-Means for Data with Tolerance introducing Penalty Term in Feature Space
Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
A new fuzzy c-means algorithms for data with tolerance is proposed by introducing a penalty term in feature space. Its idea is derived from the support vector machine introducing a penalty term for ”soft margin” in feature space. In the proposed method, the data is allowed to move for minimizing the corresponding objective function but this moveness is controlled by the penalty term. First, an optimization problem is shown by introducing tolerance with conventional fuzzy c-means algorithm in feature space. Second, Karush-Kuhn-Tucker (KKT) conditions of the optimization problem is considered. Third, an iterative algorithm is proposed by re-expressing the KKT conditions using kernel trick. Fourth, another iterative algorithm is proposed for fuzzy classification function, which shows how prototypical an arbitrary point in the data space is to the obtained each cluster by extending the membership to the whole space. Last, some numerical examples are shown.