Convergence of the symmetrical FastICA algorithm

The FastICA algorithm is one of the most popular methods to solve problems in independent component analysis (ICA) and blind source separation. It has been shown experimentally that it outperforms most of the commonly used ICA algorithms in convergence speed. A rigorous convergence analysis has been presented only for the so-called one-unit case, in which just one of the rows of the separating matrix is considered. However, in the FastICA algorithm, there is also an explicit normalization step, and it may be questioned whether the extra rotation caused by the normalization will effect the convergence speed. The purpose of this paper is to show that this is not the case and the good convergence properties of the one-unit case are also shared by the full algorithm with symmetrical normalization.