Robust low-rank covariance matrix estimation with a general pattern of missing values

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume unstructured signal models. The former can be inaccurate in...

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Bibliographic Details
Published in:Signal processing 2022-06, Vol.195, p.108460, Article 108460
Main Authors: Hippert-Ferrer, A., El Korso, M.N., Breloy, A., Ginolhac, G.
Format: Article
Language:English
Subjects:
Classification
Covariance matrix
Engineering Sciences
Expectation-maximization algorithm
Low-rank
Missing data
Mixture of scaled Gaussian
Signal and Image processing
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Summary:This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume unstructured signal models. The former can be inaccurate in real-world data sets in which heterogeneity causes heavy-tail distributions, while the latter does not profit from the usual low-rank structure of the signal. Taking advantage of both worlds, a covariance matrix estimation procedure is designed on a robust (mixture of scaled Gaussian) low-rank model by leveraging the observed-data likelihood function within an expectation-maximization algorithm. It is also designed to handle general pattern of missing values. The proposed procedure is first validated on simulated data sets. Then, its interest for classification and clustering applications is assessed on two real data sets with missing values, which include multispectral and hyperspectral time series.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2022.108460