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A Generalization to Schur's Lemma with an Application to Joint Independent Subspace Analysis

Dana Lahat 1 Christian Jutten 1 
1 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
GIPSA-DIS - Département Images et Signal
Abstract : This paper has a threefold contribution. First, it introduces a generalization to Schur's lemma from 1905 on irreducible representations. Second, it provides a comprehensive uniqueness analysis to a recently-introduced source separation model. Third, it reinforces the link between signal processing and representation theory, a field of algebra that is more often associated with quantum mechanics than signal processing. The source separation model that this paper relies on performs joint independent subspace analysis (JISA) using second order statistics. In previous work, we derived the Fisher information matrix (FIM) that corresponds to this model. The uniqueness analysis in this paper is based on analysing the FIM, where the core of the derivation is based on our proposed generalization to Schur's lemma. We provide proof both to the new lemma and to the uniqueness conditions. From a different perspective, the generalization to Schur's lemma is inspired by a coupled matrix block diagonalization problem that arises from the JISA model. The results in this paper generalize previous results about identifiability of independent vector analysis (IVA). This paper complements previously-known results on the uniqueness of joint block diagonalization (JBD) and block term decompositions (BTD), as well as of their coupled counterparts.
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Submitted on : Monday, June 6, 2016 - 9:40:25 PM
Last modification on : Wednesday, November 3, 2021 - 5:08:30 AM


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  • HAL Id : hal-01247899, version 2


Dana Lahat, Christian Jutten. A Generalization to Schur's Lemma with an Application to Joint Independent Subspace Analysis. 2016. ⟨hal-01247899v2⟩



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