On nonlinear independent component analysis using self-organizing map

Nonlinear independent component analysis (NICA) is a generalization of basic independent component analysis (ICA), and many methods have been proposed to recover signals from nonlinear mixtures. The work is performed on a post-nonlinear model, and the emphasis is focused on the method of self-organizing map (SOM). Two issues are addressed, (1) factor rotation is a crucial step in the process of inverse transform, and (2) density distortion is introduced by post-nonlinear transform. As SOM is a homeomorphism from input space to the maps, it cannot perform factor rotation and remove distortion. Experiments show that the rough nonlinear separation ability comes mostly from the decorrelation via whitening rather than from the SOM, and the process of NICA using SOM is in essence a second-order statistical method.