Identifiability conditions and subspace clustering in sparse BSS

Authors:
Pando Georgiev;Fabian Theis;Anca Ralescu
Affiliations:
Computer Science Department, University of Cincinnati, Cincinnati, OH;Institute of Biophysics, University of Regensburg, Regensburg, Germany;Computer Science Department, University of Cincinnati, Cincinnati, OH
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

Citing 5
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Abstract

We give general identifiability conditions on the source matrix in Blind Signal Separation problem. They refine some previously known ones. We develop a subspace clustering algorithm, which is a generalization of the k-plane clustering algorithm, and is suitable for separation of sparse mixtures with bigger sparsity (i.e. when the number of the sensors is bigger at least by 2 than the number of non-zero elements in most of the columns of the source matrix). We demonstrate our algorithm by examples in the square and underdetermined cases. The latter confirms the new identifiability conditions which require less hyperplanes in the data for full recovery of the sources and the mixing matrix.