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Journal Articles IEEE Signal Processing Letters Year : 2023

Probabilistic Simplex Component Analysis by Importance Sampling

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. It is based on fitting the Dirichlet parameters to the 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.
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Dates and versions

hal-04133878 , version 1 (20-06-2023)

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Nerya Granot, Tzvi Diskin, Nicolas Dobigeon, Ami Wiesel. Probabilistic Simplex Component Analysis by Importance Sampling. IEEE Signal Processing Letters, 2023, 30, pp.683-687. ⟨10.1109/LSP.2023.3282166⟩. ⟨hal-04133878⟩
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