Stationary Point Characterization for a Class of BCA Algorithms

Bounded component analysis (BCA) is a recently introduced approach including independent component analysis as a special case under the assumption of source boundedness. In this paper, we provide a stationary point analysis for the recently proposed instantaneous BCA algorithms that are capable of separating dependent, even correlated as well as independent sources from their mixtures. The stationary points are identified and characterized as either perfect separators, which are the global maxima of the proposed optimization scheme or saddle points. The important result emerging from the analysis is that there are no local optima that can prevent the proposed BCA algorithms from converging to perfect separators.