ICA 2007

ICA 2007
7th International Conference on
Independent Component Analysis
and Signal Separation

London, UK        9 - 12 September 2007

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Paper No: 140

Independent Subspace Analysis is unique, given irreducibility

Author(s): Harold Gutch, Fabian Theis

Abstract

Independent Subspace Analysis (ISA) is a generalization of ICA. It tries to find a basis in which a given random vector can be de-composed into groups of mutually independent random vectors. Since the first introduction of ISA, various algorithms to solve this problem have been introduced, however a general proof of the uniqueness of ISA decompositions remained an open question. In this contribution we address this question and sketch a proof for the separability of ISA. The key condition for separability is to require the subspaces to be not further decomposable (irreducible). Based on a decomposition into irreducible components, we formulate a general model for ISA without restrictions on the group sizes. The validity of the uniqueness result is illustrated on a toy example. Moreover, an extension of ISA to subspace extraction is introduced and its indeterminacies are discussed.

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