On the convergence behavior of the FastICA algorithm with the kurtosis cost function

The FastICA algorithm is widely used in practice for blind source separation. It would therefore be essential to have theoretical confirmation of its properties. The convergence problem in ICA is difficult and important. A rigorous convergence analysis has been presented 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 property. The global convergence analysis has been made for the 2x2 case of the FastICA algorithm with the kurtosis cost function. The purpose of this paper is to show the good convergence properties of the FastICA algorithm with symmetrical normalization for three mixtures and three sources.