Separation Theorem for K-Independent Subspace Analysis with Sufficient Conditions

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

2006-08-03

arxiv.org/abs/math/0608100v3

Mathematics

Statistics Theory

Reference [13]: corrected

Scientific paper

Here, a Separation Theorem about K-Independent Subspace Analysis (K real or complex), a generalization of K-Independent Component Analysis (KICA) is proven. According to the theorem, KISA estimation can be executed in two steps under certain conditions. In the first step, 1-dimensional KICA estimation is executed. In the second step, optimal permutation of the KICA elements is searched for. We present sufficient conditions for the KISA Separation Theorem. Namely, we shall show that (i) spherically symmetric sources (both for real and complex cases), as well as (ii) real 2-dimensional sources invariant to 90 degree rotation, among others, satisfy the conditions of the theorem.

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