Abstract
The one-bit-matching conjecture for independent component analysis (ICA) has been widely believed in the ICA community. Theoretically, it has been proved that under certain regular assumptions, the global maximum of a simplified objective function derived from the maximum likelihood or minimum mutual information criterion under the one-bit-matching condition corresponds to a feasible solution of the ICA problem, and also that all the local maxima of the objective function correspond to the feasible solutions of the ICA problem in the two-source square mixing setting. This paper further studies the one-bit-matching conjecture along this direction, and we prove that under the one-bit-matching condition there always exist many local maxima of the objective function that correspond to the stable feasible solutions of the ICA problem in the general case; moreover, in ceratin cases there also exist some local minima of the objective function that correspond to the stable feasible solutions of the ICA problem with mixed super- and sub-Gaussian sources.
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Ma, J., Chen, Z., Amari, Si. (2006). Analysis of Feasible Solutions of the ICA Problem Under the One-Bit-Matching Condition. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_104
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DOI: https://doi.org/10.1007/11679363_104
Publisher Name: Springer, Berlin, Heidelberg
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