Entropy Minima and Distribution Structural Modifications in Blind Separation of Multimodal Sources

The source separation problem is usually solved through a gradient descent on a cost function . However, may have local minima that are irrelevant from the source separation point of view in particular when the source distribution is multimodal. Cardoso explained the reason for such spurious minima when a likelihood-based function is used as cost criterion, even when the source distributions are a priori known.This paper shows that such spurious minima may also appear when using the marginal entropy cost function; it aims to draw an intuitive justification about the existence and the locations of these minima when dealing with multimodal sources. This justification is based on a structural modification (mainly the modality) analysis of the output distribution according to the mixing coefficients.