Extraction of Local Independent Components by Using Fuzzy c-Varieties

Abstract

Even though Independent Component Analysis (ICA) has become an important technique for Blind Source Separation (BSS), it can provide only a crude approximation for general nonlinear data distributions. Karhunen et al. proposed Local ICA, in which K-means clustering method was used before the application of linear ICA. The clustering part was responsible for an overall coarse nonlinear representation of the underlying data, while linear independent components of each cluster were used for describing local features of the data. In this paper, we propose a method for extracting local independent components by using Fuzzy c-Varieties (FCV) clustering, which seems to be more natural than K-means or the like. Because FCV can be regarded as a simultaneous approach to clustering and Principal Component Analysis (PCA), the FCV takes part of the preprocessing of Fast ICA by Hyvarinen et al..