Identifiability of second-order multidimensional ICA

Dana Lahat, Jean François Cardoso, Hagit Messer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper, we consider the identifiability of second-order blind separation of multidimensional components. By maximizing the likelihood for piecewise-stationary Gaussian data, we obtain that the maximum likelihood (ML) solution is equivalent to joint block diagonalization (JBD) of the sample covariance matrices of the observations. Small-error analysis of the solution indicates that the identifiability of the model depends on the positive-definiteness of a matrix, which is a function of the latent source covariance matrices. By analysing this matrix, we derive necessary and sufficient conditions for the model to be identifiable. These are also the sufficient and necessary conditions for JBD of any set of real positive-definite symmetric matrices to be unique.

Original languageEnglish
Title of host publicationProceedings of the 20th European Signal Processing Conference, EUSIPCO 2012
Number of pages5
StatePublished - 2012
Externally publishedYes
Event20th European Signal Processing Conference, EUSIPCO 2012 - Bucharest, Romania
Duration: 27 Aug 201231 Aug 2012

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491


Conference20th European Signal Processing Conference, EUSIPCO 2012


  • Joint block diagonalization
  • identifiability
  • multidimensional ICA
  • uniqueness


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