Optimal performance of second-order multidimensional ICA

Dana Lahat*, Jean Francois Cardoso, Hagit Messer

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

Independent component analysis (ICA) and blind source separation (BSS) deal with extracting mutually-independent elements from their observed mixtures. In "classical" ICA, each component is one- dimensional in the sense that it is proportional to a column of the mixing matrix. However, this paper considers a more general setup, of multidimensional components. In terms of the underlying sources, this means that the source covariance matrix is block-diagonal rather than diagonal, so that sources belonging to the same block are correlated whereas sources belonging to different blocks are uncorrelated. These two points of view -correlated sources vs. multidimensional components- are considered in this paper. The latter offers the benefit of providing a unique decomposition. We present a novel, closed-form expression for the optimal performance of second-order ICA in the case of multidimensional elements. Our analysis is verified through numerical experiments.

Original languageEnglish
Pages (from-to)50-57
Number of pages8
JournalLecture Notes in Computer Science
Volume5441
DOIs
StatePublished - 2009
Event8th International Conference on Independent Component Analysis and Signal Separation, ICA 2009 - Paraty, Brazil
Duration: 15 Mar 200918 Mar 2009

Keywords

  • Blind source separation
  • Correlated sources
  • Independent component analysis
  • Joint block diagonalization
  • Multidimensional components
  • Performance analysis

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