F.J. Theis and E.W. Lang (Germany), and F. Rojas and C.G. Puntonet (Spain)
geometric independent component analysis, blind sourceseparation, overcomplete independent component analysis
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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