Connecting geometric independent component analysis to unsupervised learning algorithms

Abstract

The goal of independent component analysis (ICA) lies in transforming a mixed random vector in order to render it as independent as possible. This paper shows how to use adaptive learning and clustering algorithms to approximate mixture space densities thus learning the mixing model. Here, a linear square-model is assumed, and as learning algorithm either a self-organizing map (SOM) or a neural gas (NG) is used. These result in a considerable improvement in separation quality in comparison to other mixture-space analysis ('geometric') algorithms, although the computational cost is rather high. By establishing this connection between neural networks and ICA, applications like for example transferring convergence proofs for SOMs to geometric ICA algorithms now seem possible.