Fuzzy c-Means Clustering for Data with Clusterwise Tolerance Based on L2– and L1-Regularization
Yukihiro Hamasuna*,**, Yasunori Endo**, and Sadaaki Miyamoto**
*Research Fellow of the Japan Society for the Promotion of Science
**Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
Detecting various kinds of cluster shape is an important problem in the field of clustering. In general, it is difficult to obtain clusters with different sizes or shapes by single-objective function. From that sense, we have proposed the concept of clusterwise tolerance and constructed clustering algorithms based on it. In the field of data mining, regularization techniques are used in order to derive significant classifiers. In this paper, we propose another concept of clusterwise tolerance from the viewpoint of regularization. Moreover, we construct clustering algorithms for data with clusterwise tolerance based on L2– and L1-regularization. After that, we describe fuzzy classification functions of proposed algorithms. Finally, we show the effectiveness of proposed algorithms through numerical examples.
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