Unsupervised linear component analysis for a class of probability mixture models
Abstract
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.
Keywords
Cite
@article{arxiv.2312.07975,
title = {Unsupervised linear component analysis for a class of probability mixture models},
author = {Marc Castella},
journal= {arXiv preprint arXiv:2312.07975},
year = {2023}
}