NONLINEAR INDEPENDENT COMPONENT ANALYSIS(ICA) USING POWER SERIES AND APPLICATION TO BLIND SOURCE SEPARATION
Ziyou Xiong, Thomas S. Huang · 2001
that generalizes Bell & Sejnowski's classic ICA to tackle nonlinear ICA and the introduction of a new and efficient form of "natural gradient". This algorithm uses power series of non-linear mixtures to approximate the Taylor expansion of the inverse function mapping from sources to mixtures. The approximation enables derivation of learning rules for weight matrix associated with power series of any order. When applied to blind source separation, it successfully separated non-linear mixtures for which Bell & Sejnowski's algorithm could not due to its linear mixture model. In separating linear mixtures using this algorithm, the weight matrices for higher order mixtures converge to zero matrix. This is consistent with intuition, suggesting the validity of the generalization.