Separation Theorem for Independent Subspace Analysis with Sufficient Conditions

Details Separation Theorem for Independent Subspace Analysis with Sufficient Conditions Separation Theorem for Independent Subspace Analysis with Sufficient Conditions

2006-03-22

arxiv.org/abs/math/0603535v2

Mathematics

Statistics Theory

11 pages, 0 figures

Scientific paper

Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the first step, 1-dimensional ICA estimation is executed. In the second step, optimal permutation of the ICA elements is searched for. We present sufficient conditions for the ISA Separation Theorem. Namely, we shall show that (i) elliptically symmetric sources, (ii) 2-dimensional sources invariant to 90 degree rotation, among others, satisfy the conditions of the theorem.

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