The nonlinear PCA criterion in blind source separation: Relations with other approaches

We present new results on the nonlinear PCA (Principal Component Analysis) criterion in blind source separation (BSS). We derive the criterion in a form that allows easy comparisons with other BSS and Independent Component Analysis (ICA) contrast functions like cumulants, Bussgang criteria, and information theoretic contrasts. This clariies how the nonlinearity should be chosen optimally. We also discuss the connections of the nonlinear PCA learning rule with the Bell-Sejnowski algorithm and the adaptive EASI algorithm. Furthermore, we show that a nonlinear PCA criterion can be minimized using least-squares approaches, leading to computationally eecient and fast converging algorithms. The paper shows that nonlinear PCA is a versatile starting point for deriving diierent kinds of algorithms for blind signal processing problems.