Independent Subspace Analysis Is Unique, Given Irreducibility

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4666)


Independent Subspace Analysis (ISA) is a generalization of ICA. It tries to find a basis in which a given random vector can be decomposed 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.


Random Vector Independent Component Irreducible Component Independent Component Analysis Invertible Matrix 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Max Planck Institute for Dynamics and Self-Organization, 37073 GöttingenGermany

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