Block component analysis, a new concept for blind source separation

Authors:
Lieven De Lathauwer
Affiliations:
Katholieke Universiteit Leuven Campus Kortrijk, Kortrijk, Belgium
Venue:
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Year:
2012

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Abstract

The fact that the decomposition of a matrix in a minimal number of rank-1 terms is not unique, leads to a basic indeterminacy in factor analysis. Factors and loadings are only unique under certain assumptions. Working in a multilinear framework has the advantage that the decomposition of a higher-order tensor in a minimal number of rank-1 terms (its Canonical Polyadic Decomposition (CPD)) is unique under mild conditions. We have recently introduced Block Term Decompositions (BTD) of a higher-order tensor. BTDs write a given tensor as a sum of terms that have low multilinear rank, without having to be rank-1. In this paper we explain how BTDs can be used for factor analysis and blind source separation. We discuss links with Canonical Polyadic Analysis (CPA) and Independent Component Analysis (ICA). Different variants of the approach are illustrated with examples.