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Robust Sparse Component Analysis Based on a Generalized Hough Transform

  • Fabian J. TheisEmail author
  • Pando Georgiev
  • Andrzej Cichocki
Open Access
Research Article
Part of the following topical collections:
  1. Advances in Blind Source Separation

Abstract

An algorithm called Hough SCA is presented for recovering the matrix Open image in new window in Open image in new window , where Open image in new window is a multivariate observed signal, possibly is of lower dimension than the unknown sources Open image in new window . They are assumed to be sparse in the sense that at every time instant Open image in new window , Open image in new window has fewer nonzero elements than the dimension of Open image in new window . The presented algorithm performs a global search for hyperplane clusters within the mixture space by gathering possible hyperplane parameters within a Hough accumulator tensor. This renders the algorithm immune to the many local minima typically exhibited by the corresponding cost function. In contrast to previous approaches, Hough SCA is linear in the sample number and independent of the source dimension as well as robust against noise and outliers. Experiments demonstrate the flexibility of the proposed algorithm.

Keywords

Information Technology Cost Function Local Minimum Quantum Information Nonzero Element 

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Copyright information

© Fabian J. Theis et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Fabian J. Theis
    • 1
    Email author
  • Pando Georgiev
    • 2
  • Andrzej Cichocki
    • 3
    • 4
  1. 1.Institute of BiophysicsUniversity of RegensburgRegensburgGermany
  2. 2.ECECS Department and Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  3. 3.BSI RIKEN, Laboratory for Advanced Brain Signal ProcessingWako, SaitamaJapan
  4. 4.Faculty of Electrical EngineeringWarsaw University of TechnologyWarsawPoland

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