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To Infinity and Beyond: On ICA over Hilbert Spaces

  • Harold W. Gutch
  • Fabian J. Theis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7191)

Abstract

The original Independent Component Analysis (ICA) problem of blindly separating a mixture of a finite number of real-valued statistically independent one-dimensional sources has been extended in a number of ways in recent years. These include dropping the assumption that all sources are one-dimensional and some extensions to the case where the sources are not real-valued. We introduce an extension in a further direction, no longer assuming only a finite number of sources, but instead allowing infinitely many. We define a notion of independent sources for this case and show separability of ICA in this framework.

Keywords

Hilbert Space Random Vector Independent Component Analysis Dimensional Case Real Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Comon, P.: Independent component analysis - a new concept? Signal Processing 36, 287–314 (1994)CrossRefzbMATHGoogle Scholar
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    Bonaccorsi, S., Priola, E.: From Brownian Motion to Stochastic Differential Equations. In: 10th Internet SeminarGoogle Scholar
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    da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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