ICA by Nonlinear Decorrelation and Nonlinear PCA
Aapo Hyvärinen, Juha Karhunen, Erkki Oja · 2001
This chapter starts by reviewing some of the early research efforts in independent component analysis (ICA), especially the technique based on nonlinear decorrelation, that was successfully used by Jutten, Hérault, and Ans to solve the first ICA problems. The authors show that independent components can in some cases be found as nonlinearly uncorrelated linear combinations. The nonlinear functions used in this approach introduce higher order statistics into the solution method, making ICA possible. Another approach to ICA that is related to PCA is the so-called nonlinear PCA. The authors review the nonlinear PCA criterion and show its equivalence to other criteria like maximum likelihood (ML).