On Kernelized Fuzzy c-Means Clustering for Uncertain Data with L₂ and L₁ Regularization Terms of Penalty Vectors Using Explicit Mapping

Abstract

Recently, in clustering which means a unsupervised classification method, the one with kernel function is remarkable because we can easily calculate inner products of data which are map from the pattern space to a high-dimensional feature space. Moreover, a clustering method with penalty vectors is proposed as of the methods to handle uncertain data. This method can naturally formulate uncertainty to optimization problem. In this paper, we propose a new clustering algorithm with penalty vectors and kernel function. The proposed method can calculate cluster centers and penalty vectors in feature space directly by using explicit mapping to the high-dimensional feature space. We use L2 and L1 regularization terms to introduce penalty vectors.