An alternative natural gradient approach for ICA based learning algorithms in blind source separation

In this paper a new formula for natural gradient based learning in blind source separation (BSS) problem is derived. This represents a different gradient from the usual one in [1], but can still considered natural since it comes from the definition of a Riemannian metric in the matrix space of parameters. The new natural gradient consists on left multiplying the standard gradient for an adequate term depending on the parameter matrix to adapt, whereas the other one considers a right multiplication. The two natural gradients have been employed in two ICA based learning algorithms for BSS and it resulted they have identical behavior.