Separation theorem for independent subspace analysis and its consequences

Zoltán Szabó, Barnabás Póczos, A. Lőrincz

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Independent component analysis (ICA) the theory of mixed, independent, non-Gaussian sources has a central role in signal processing, computer vision and pattern recognition. One of the most fundamental conjectures of this research field is that independent subspace analysis (ISA) the extension of the ICA problem, where groups of sources are independent can be solved by traditional ICA followed by grouping the ICA components. The conjecture, called ISA separation principle, (i) has been rigorously proven for some distribution types recently, (ii) forms the basis of the state-of-the-art ISA solvers, (iii) enables one to estimate the unknown number and the dimensions of the sources efficiently, and (iv) can be extended to generalizations of the ISA task, such as different linear-, controlled-, post nonlinear-, complex valued-, partially observed problems, as well as to problems dealing with nonparametric source dynamics. Here, we shall review the advances on this field.

Original languageEnglish
Pages (from-to)1782-1791
Number of pages10
JournalPattern Recognition
Volume45
Issue number4
DOIs
Publication statusPublished - Apr 2012

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Independent component analysis
Computer vision
Pattern recognition
Signal processing

Keywords

  • Complex valued models
  • Controlled models
  • Independent subspace analysis
  • Linear systems
  • Nonparametric source dynamics
  • Partially observed systems
  • Post nonlinear systems
  • Separation principles

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Computer Vision and Pattern Recognition
  • Signal Processing

Cite this

Separation theorem for independent subspace analysis and its consequences. / Szabó, Zoltán; Póczos, Barnabás; Lőrincz, A.

In: Pattern Recognition, Vol. 45, No. 4, 04.2012, p. 1782-1791.

Research output: Contribution to journalArticle

Szabó, Zoltán ; Póczos, Barnabás ; Lőrincz, A. / Separation theorem for independent subspace analysis and its consequences. In: Pattern Recognition. 2012 ; Vol. 45, No. 4. pp. 1782-1791.
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