A geometric algorithm for overcomplete linear ICA

Fabian J. Theis, Elmar W. Lang, Carlos G. Puntonet

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


Geometric algorithms for linear square independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (Neural Process. Lett. 2 (1995), Signal Processing 46 (1995) 267) in order to separate linear mixtures. We generalize these algorithms to overcomplete cases with more sources than sensors. With geometric ICA we get an efficient method for the matrix-recovery step in the framework of a two-step approach to the source separation problem. The second step-source-recovery-uses a maximum-likelihood approach. There we prove that the shortest-path algorithm as proposed by Bofill and Zibulevsky (in: P. Pajunen, J. Karhunen (Eds.), Independent Component Analysis and Blind Signal Separation (Proceedings of ICA'2000), 2000, pp. 87-92) indeed solves the maximum-likelihood conditions.

Original languageEnglish
Pages (from-to)381-398
Number of pages18
Issue number1-4
StatePublished - Jan 2004
Externally publishedYes


  • Geometric independent component analysis
  • Overcomplete blind source separation
  • Overcomplete independent component analysis
  • Overcomplete representation


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