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To Infinity and Beyond: On ICA over Hilbert Spaces

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Part of the Lecture Notes in Computer Science book series (LNTCS,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

  1. Comon, P.: Independent component analysis - a new concept? Signal Processing 36, 287–314 (1994)

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  2. Bonaccorsi, S., Priola, E.: From Brownian Motion to Stochastic Differential Equations. In: 10th Internet Seminar

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  3. da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press (1992)

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© 2012 Springer-Verlag Berlin Heidelberg

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Gutch, H.W., Theis, F.J. (2012). To Infinity and Beyond: On ICA over Hilbert Spaces. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-28551-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28550-9

  • Online ISBN: 978-3-642-28551-6

  • eBook Packages: Computer ScienceComputer Science (R0)