A New Independent Component Analysis Algorithm Based on Extended-Natural Gradient

In this paper, a new extended concept of directional derivative named extend-directional derivative, which is a reasonable extension of the conventional derivative, is induced based on the old counterpart. Meanwhile, with this similar method, using this extension in BSS problems and ICA based algorithms, a new concept named extended-natural gradient, whose specific form depends on a translation function on the independent variable matrix, is brought forward to solve the puzzle we have been facing. With the assist of ICALAB software package, we conduct these new algorithms, observe the actual separation effect and analyze the performance and convergence rate of them, all of which are tested in MATLAB simulation environment. The results show that, with proper translation function chosen, extended algorithm converges much faster than conventional natural gradient algorithm. No doubt this is a great improvement from the view of accelerate the execution of natural gradient algorithm, as well as in deeply research in the natural gradient algorithm itself and delivering new algorithms to solve the blind separation problems.