To Infinity and Beyond: On ICA over Hilbert Spaces

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7191)


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.


Hilbert Space Random Vector Independent Component Analysis Dimensional Case Real Hilbert Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  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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