To infinity and beyond: on ICA over hilbert spaces

  • Authors:

  • Harold W. Gutch;Fabian J. Theis

  • Affiliations:

  • Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany;Technical University Munich, Germany

  • Venue:
  • LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
  • Year:
  • 2012

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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.