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Information theoretic versus cumulant-based contrasts for multimodal source separation

Recently, several authors have emphasized the existence of spurious maxima in usual contrast functions for source separation (e.g., the likelihood and the mutual information) when several sources have multimodal distributions. The aim of this letter is to compare the information theoretic contrasts to cumulant-based ones from the robustness to spurious maxima point of view. Even if all of them tend to measure, in some way, the same quantity, which is the output independence (or equivalently, the output non-Gaussianity), it is shown that in the case of a mixture involving two sources, the kurtosis-based contrast functions are more robust than the information theoretic ones when the source distributions are multimodal.