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Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2023

A Robust and Flexible EM Algorithm for Mixtures of Elliptical Distributions with Missing Data

Résumé

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or have non-Gaussian distributions. To overcome this issue, a new EM algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of angular Gaussian distributions under generic assumptions (i.e., each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework with missing data thanks to its conditional distribution, which is shown to be a multivariate t-distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on realworld datasets show that this algorithm is very competitive when compared to other classical imputation methods.
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hal-04317202 , version 1 (10-04-2024)

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Florian Mouret, Alexandre Hippert-Ferrer, Frédéric Pascal, Jean-Yves Tourneret. A Robust and Flexible EM Algorithm for Mixtures of Elliptical Distributions with Missing Data. IEEE Transactions on Signal Processing, 2023, 71, pp.1--25. ⟨10.1109/TSP.2023.3267994⟩. ⟨hal-04317202⟩
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