Non-linear ICA by using isometric dimensionality reduction

Abstract

In usual ICA methods, sources are typically estimated by maximizing a measure of their statistical independence. This paper explains how to perform non-linear ICA by preprocessing the mixtures with recent non-linear dimensionality reduction techniques. These techniques are intended to produce a low-dimensional representation of the data (the mixtures), which is isometric to their initial high-dimensional distribution. A detailed study of the mixture model that makes the separation possible precedes a practical example. © Springer-Verlag 2004.