Separation Theorem for K-Independent Subspace Analysis with Sufficient Conditions
نویسندگان
چکیده
Abstract. Here, a Separation Theorem about K-Independent Subspace Analysis (K ∈ {R,C} real or complex), a generalization of K-Independent Component Analysis (K-ICA) is proven. According to the theorem, K-ISA estimation can be executed in two steps under certain conditions. In the first step, 1-dimensional K-ICA estimation is executed. In the second step, optimal permutation of the K-ICA elements is searched for. We present sufficient conditions for the K-ISA 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 rotation, among others, satisfy the conditions of the theorem.
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