Unsupervised Linear Component Analysis for a Class of Probability Mixture Models

We deal with a model where a set of observations is obtained by a linear superposition of unknown components called sources. The problem consists in recovering the sources without knowing the linear transform. We extend the well-known Independent Component Analysis (ICA) methodology. Instead of assuming independent source components, we assume that the source vector is a probability mixture of two distributions. Only one distribution satisfies the ICA assumptions, while the other one is concentrated on a specific but unknown support. Sample points from the latter are clustered based on a data-driven distance in a fully unsupervised approach. A theoretical grounding is provided through a link with the Christoffel function. Simulation results validate our approach and illustrate that it is an extension of a formerly proposed method.