ICA in boolean XOR mixtures

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Abstract

We consider Independent Component Analysis (ICA) for the case of binary sources, where addition has the meaning of the boolean "Exclusive Or" (XOR) operation. Thus, each mixture-signal is given by the XOR of one or more of the source-signals. While such mixtures can be considered linear transformations over the finite Galois Field of order 2, they are certainly nonlinear over the field of real-valued numbers, so classical ICA principles may be inapplicable in this framework. Nevertheless, we show that if none of the independent random sources is uniform (i.e., neither one has probability 0.5 for 1/0), then any invertible mixing is identifiable (up to permutation ambiguity). We then propose a practical deflation algorithm for source separation based on entropy minimization, and present empirical performance results by simulation.

Original languageEnglish
Title of host publicationIndependent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings
PublisherSpringer Verlag
Pages827-835
Number of pages9
ISBN (Print)9783540744931
DOIs
StatePublished - 2007
Event7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 - London, United Kingdom
Duration: 9 Sep 200712 Sep 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4666 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007
Country/TerritoryUnited Kingdom
CityLondon
Period9/09/0712/09/07

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