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Extraction of Local Independent Components Using Fuzzy Clustering

Even though Independent Component Analysis (ICA) has become an important technique for Blind Source Separation (BSS), it can provide a crude approximation only for general nonlinear data distributions. Karhunen et al. proposed Local ICA, in which K-means clustering method was performed before the application of linear ICA. The clustering part was responsible for an overall coarse nonlinear representation of the underlying data, while linear ICA models 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, that seems to be more useful than K-means or the like. Because FCV can be regarded as the simultaneous approach to clustering and Principal Component Analysis (PCA), the FCV performs as a preprocessing of Fast ICA by Hyvärinen et al..