This chapter deals with independent component analysis and blind source separation for nonlinear data models. A fundamental difficulty, especially in the nonlinear ICA problem, is that it is highly non-unique without a suitable regularization. After considering this, two methods for solving the nonlinear ICA and BSS problems are presented in more detail. The first one is a maximum likelihood method based on a modified generative topographic mapping. The second approach applies Bayesian ensemble learning to a flexible multi-layer perceptron model for finding the sources and nonlinear mixing mapping that have most probably given rise to the observed mixed data. Finally, other techniques introduced for the nonlinear ICA and BSS problems are briefly reviewed.

Introduction

Independent Component Analysis [Lee, 1998, Oja et al., 1997, Girolami, 1999bl is a statistical technique which tries to represent the observed data in terms of statistically independent component variables. ICA is closely related to the blind source separation (BSS) problem [Cardoso, 1998a, Amari et al., 1996, Lee, 1998, Oja et al., 1997, Girolami, 1999b1, where the general goal is to separate mutually independent but otherwise unknown source signals from their observed mixtures without knowing the mixing process.