On the convergence of ICA algorithms with symmetric orthogonalization

We study the convergence behavior of independent component analysis (ICA) algorithms that are based on the contrast function maximization and that employ symmetric orthogonalization method to guarantee the orthogonality property of the search matrix. In particular, the characterization of the critical points of the corresponding optimization problem and the stationary points of the conventional gradient ascent and fixed point algorithms are obtained. As an interesting and a useful feature of the symmetrical orthogonalization method, we show that the use of symmetric orthogonalization enables the monotonic convergence for the fixed point ICA algorithms that are based on the convex contrast functions.