Stability Analysis of Natural Gradient Learning Rules in Complete ICA: A Unifying Perspective

This letter deals with the independent component analysis (ICA) problem in the complete case. As appeared recently in the literature, different Riemannian metrics can be defined within the parameter space (i.e., the general linear group), allowing to derive correspondingly various ICA learning rules based on the relative natural gradients (NGs). This letter proposes a general framework to analyze the stability of such learning rules, including the already published study focusing on the Amari's NG approach as a special case thereof. In particular, it is shown that the stability conditions known in the literature still hold in all cases addressed