Kernel Principal Component Analysis for Fuzzy Point Data Set

Abstract

Kernel principal component analysis (KPCA) has provided an extremely powerful approach to extracting nonlinear features via kernel trick, and it has been suggested for a number of applications. Whereas the nonlinearity can be allowed by the utilization of Mercer kernels, the standard KPCA could only process exact training samples which be treated uniformly and can't reflect prior information of data. However, in many real-world applications, each training data has different meanings and confidence degrees for population. In this paper, a new concept, called "fuzzy point data" which is defined by giving a fuzzy membership to each training sample, is proposed for helping us handle the confidence of data. We reformulate KPCA for fuzzy point data. Experimental results show our method could embody effects of different samples in constructing principal axes and supply a feasible method to control possible outliers.