Spurious Solution of the Maximum Likelihood Approach to ICA

For the separation of linear instantaneous mixtures of independent sources, many Independent Component Analysis (ICA) algorithms can learn the separating matrix by optimizing some objective functions derived from various criteria. The Maximum Likelihood (ML) principle, with hypothesized model pdf's, provides an objective function which is commonly used. It is generally considered that the ML approach leads to a separating solution as long as the kurtosis signs of the model pdf's can correspond and equal to those of the sources, respectively, in some order, which is referred to as the one-bit-matching condition. In this letter, we present an experimental analysis on spurious solution of the ML approach and show that spurious maximum of the objective function really exists in certain cases even if the one-bit-matching condition is satisfied.