One-Bit-Matching Conjecture for Independent Component Analysis
Neural Computation
A Constrained EM Algorithm for Independent Component Analysis
Neural Computation
Analysis of the Kurtosis-Sum Objective Function for ICA
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
A step by step optimization approach to independent component analysis
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Two adaptive matching learning algorithms for independent component analysis
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
A one-bit-matching learning algorithm for independent component analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Analysis of feasible solutions of the ICA problem under the one-bit-matching condition
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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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 the assumption of zero skewness for the model probability density functions, the global maximum of a cost function derived from the typical objective function on the ICA problem with the one-bit-matching condition corresponds to a feasible solution of the ICA problem. In this note, we further prove that all the local maximums of the cost function correspond to the feasible solutions of the ICA problem in the two-source case under the same assumption. That is, as long as the one-bit-matching condition is satisfied, the two-source ICA problem can be successfully solved using any local descent algorithm of the typical objective function with the assumption of zero skewness for all the model probability density functions.