Probabilistic Simplex Component Analysis by Importance Sampling

TL;DR

This paper introduces an EM algorithm with importance sampling for probabilistic simplex component analysis, offering a computationally efficient alternative to previous geometrical and variational methods, especially effective at high SNR.

Contribution

It presents a novel EM-based approach with importance sampling using a LMMSE surrogate distribution for probabilistic simplex component analysis.

Findings

Outperforms state-of-the-art methods in numerical experiments

Effective at high signal-to-noise ratios

Provides a computationally efficient solution

Abstract

In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this challenging problem were based on geometrical approaches or computationally intensive variational methods. In contrast, we propose a conventional expectation maximization (EM) algorithm which embeds importance sampling. For this purpose, the proposal distribution is chosen as a simple surrogate distribution of the target posterior that is guaranteed to lie in the simplex. This distribution is based on the Gaussian linear minimum mean squared error (LMMSE) approximation which is accurate at high signal-to-noise ratio. Numerical experiments in different settings demonstrate the advantages of this adaptive surrogate over state-of-the-art methods.