TY - GEN

T1 - ICA in boolean XOR mixtures

AU - Yeredor, Arie

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38148999579&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-74494-8_103

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

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AN - SCOPUS:38148999579

SN - 9783540744931

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 827

EP - 835

BT - Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings

PB - Springer Verlag

T2 - 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007

Y2 - 9 September 2007 through 12 September 2007

ER -