Efficient geometric methods for kernel density estimation based Independent Component Analysis

The performance of Independent Component Analysis (ICA) methods significantly depends on the choice of the contrast function and the optimisation algorithm used in obtaining the demixing matrix. It has been shown that nonparametric ICA approaches are more robust than its parametric counterparts. One basic nonparametric ICA contrast was developed by approximating mutual information using kernel density estimations. In this work we study the kernel density estimation based linear ICA problem from an optimisation point of view. Two geometric methods are proposed to optimise the kernel density estimation based linear ICA contrast function, a Jacobi-type method and an approximate Newton-like method. Rigorous analysis shows that both geometric methods converge locally quadratically fast to the correct demixing. The performance of the proposed algorithms is investigated by numerical experiments.