LVQ Clustering and SOM Using a Kernel Function

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  • INOKUCHI Ryo
    Risk Engineering Major, Graduate School of Systems and Information Engineering, University of Tsukuba
  • MIYAMOTO Sadaaki
    Risk Engineering Major, Graduate School of Systems and Information Engineering, University of Tsukuba

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  • カーネル関数を利用したLVQクラスタリングとSOM
  • カーネル カンスウ オ リヨウ シタ LVQ クラスタリング ト SOM

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Abstract

This paper aims at discussing a clustering algorithm based on Learning Vector Quantization (LVQ) using a kernel function in support vector machines. Mapping object data into the high-dimensional feature space, this algorithm can find nonlinear boundaries between clusters which ordinary algorithms cannot find. The reason why kernel-based algorithms can find nonlinear clusters is that they may be linearly separated in the high-dimensional feature space. Nevertheless, actual configuration of data units in the high-dimensional feature space is unknown. Self-Organizing Map (SOM) associated with LVQ is hence applied with a kernel function. The resulting topological map for data in the high-dimensional feature space can visualize linearly separated clusters found by the proposed method. Numerical examples are given to show effectiveness of the proposed method when compared with fuzzy c-means and kernel-based fuzzy c-means.

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