Extending Geometric ICA to Overcomplete and High-dimensional BSS-Problems

F.J. Theis and E.W. Lang (Germany), and F. Rojas and C.G. Puntonet (Spain)

Keywords

geometric independent component analysis, blind sourceseparation, overcomplete independent component analysis

Abstract

In geometric independent component analysis (geoICA) [10] linear mixtures are separated by analysis of the ’geometry’ of the mixture scatterplot. Geometric algorithms, however, require an exponentially rising number of samples and convergence times with increasing dimensionality; this practically restricts geoICA to low-dimensional cases. In this paper we introduce overcomplete geoICA as a generalization of the standard geometric algorithm to overcomplete cases with more sources than sensors. In the framework of a two-step approach to the blind source separation (BSS) problem geoICA offers an efficient method for the matrix-recovery step . The second step — source recovery — uses a maximum-likelihood approach. We then use this overcomplete geoICA algorithm to reduce high dimensional problems to lower-dimensional ones, thus effectively generalizing geoICA to higher dimensions.

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