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. © Springer-Verlag Berlin Heidelberg 2007.

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Yeredor, A. (2007). ICA in boolean XOR mixtures. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4666 LNCS, pp. 827–835). Springer Verlag. https://doi.org/10.1007/978-3-540-74494-8_103

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