Local Separation Property of the Two-Source ICA Problem with the One-Bit-Matching Condition

Abstract

The one-bit-matching conjecture for independent component analysis (ICA) is basically stated as “all the sources can be separated as long as there is one-to-one same-sign-correspondence between the kurtosis signs of all source probability density functions (pdf’s) and the kurtosis signs of all model pdf’s”, which has been widely believed in the ICA community, but not proved completely. Recently, it has been proved that under the assumption of zero skewness for the model pdf’s, the global maximum of a cost function on the ICA problem with the one-bit-matching condition corresponds to a feasible solution of the ICA problem. In this paper, we further study the one-bit-matching conjecture along this direction and prove that all the possible local maximums of this cost function correspond to the feasible solutions of the ICA problem in the case of two sources under the same assumption. That is, the one-bit-matching condition is sufficient for solving the two-source ICA problem via any local ascent algorithm of the cost function.