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 -