Local minima of information-theoretic criteria in blind source separation

Recent simulation results have indicated that spurious minima in information-theoretic criteria with an orthogonality constraint for blind source separation may exist. Nevertheless, those results involve approximations (e.g., density estimation), so that they do not constitute an absolute proof. In this letter, the problem is tackled from a theoretical point of view. An example is provided for which it is rigorously proved that spurious minima can exist in both mutual information and negentropy optima. The proof is based on a Taylor expansion of the entropy.