ICA in boolean XOR mixtures

Arie Yeredor

doi:10.1007/978-3-540-74494-8_103

ICA in boolean XOR mixtures

Arie Yeredor

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings
Publisher	Springer Verlag
Pages	827-835
Number of pages	9
ISBN (Print)	9783540744931
DOIs	https://doi.org/10.1007/978-3-540-74494-8_103
State	Published - 2007
Event	7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 - London, United Kingdom Duration: 9 Sep 2007 → 12 Sep 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4666 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007
Country/Territory	United Kingdom
City	London
Period	9/09/07 → 12/09/07

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10.1007/978-3-540-74494-8_103

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Yeredor, A. (2007). ICA in boolean XOR mixtures. In Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings (pp. 827-835). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4666 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74494-8_103

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title = "ICA in boolean XOR mixtures",

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.",

author = "Arie Yeredor",

year = "2007",

doi = "10.1007/978-3-540-74494-8_103",

language = "אנגלית",

isbn = "9783540744931",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

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booktitle = "Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings",

note = "null ; Conference date: 09-09-2007 Through 12-09-2007",

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Yeredor, A 2007, ICA in boolean XOR mixtures. in Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4666 LNCS, Springer Verlag, pp. 827-835, 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007, London, United Kingdom, 9/09/07. https://doi.org/10.1007/978-3-540-74494-8_103

ICA in boolean XOR mixtures. / Yeredor, Arie.

Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings. Springer Verlag, 2007. p. 827-835 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4666 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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ICA in boolean XOR mixtures

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