Second Order Subspace Analysis and Simple Decompositions

  • Harold W. Gutch
  • Takanori Maehara
  • Fabian J. Theis
Conference paper

DOI: 10.1007/978-3-642-15995-4_46

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6365)
Cite this paper as:
Gutch H.W., Maehara T., Theis F.J. (2010) Second Order Subspace Analysis and Simple Decompositions. In: Vigneron V., Zarzoso V., Moreau E., Gribonval R., Vincent E. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2010. Lecture Notes in Computer Science, vol 6365. Springer, Berlin, Heidelberg

Abstract

The recovery of the mixture of an N-dimensional signal generated by N independent processes is a well studied problem (see e.g. [1,10]) and robust algorithms that solve this problem by Joint Diagonalization exist. While there is a lot of empirical evidence suggesting that these algorithms are also capable of solving the case where the source signals have block structure (apart from a final permutation recovery step), this claim could not be shown yet - even more, it previously was not known if this model separable at all. We present a precise definition of the subspace model, introducing the notion of simple components, show that the decomposition into simple components is unique and present an algorithm handling the decomposition task.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Harold W. Gutch
    • 1
    • 2
  • Takanori Maehara
    • 3
  • Fabian J. Theis
    • 2
    • 4
  1. 1.Department of Nonlinear DynamicsMax Planck Institute for Dynamics and Self-OrganizationGermany
  2. 2.Technical University of MunichGermany
  3. 3.University of TokyoJapan
  4. 4.Helmholtz-Institute NeuherbergGermany

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