A post nonlinear geometric algorithm for independent component analysis.

Abstract

Simple linear independent component analysis (ICA) algorithms work efficiently only in linear mixing environments. Whereas, a nonlinear ICA model, which is more complicated, would be more practical for general applications as it can work with both linear and nonlinear mixtures. In this paper, we introduce a novel method for nonlinear ICA problem. The proposed method follows the post nonlinear approach to model the mixtures, and exploits the difference between a linear mixture and a nonlinear one from their nature of distributions in a multidimensional space to develop a separation scheme. The nonlinear mixture is represented by a nonlinear surface while the linear mixture is represented by a plane. A geometric learning algorithm named as post nonlinear geometric ICA (pnGICA) is developed by geometrically transforming the nonlinear surface to a plane, i.e., to a linear mixture. Computer simulations of the algorithm provide promising performance on different data sets.