On the difference between updating the mixing matrix and updating the separation matrix

When the ICA source separation problem is solved by maximum likelihood, a proper choice of the parameters is important. A comparison has been performed between the use of a mixing matrix and the use of the separation matrix as parameters in the likelihood. By looking at a general behavior of the cost function as function of the mixing matrix or as function of the separation matrix, it is explained and illustrated why it is better to select the separation matrix as a parameter than to use the mixing matrix as a parameter. The behavior of the natural gradient in the two cases has been considered as well as the influence of pre-whitening.