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

arXiv: https://arxiv.org/abs/2107.10505 · HTML: https://mlsanity.com/paper/2107.10505/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2021.

## Built on by (most cited first, 8 of 8)

- [The Fisher-Rao geometry of CES distributions](https://mlsanity.com/paper/2310.01032/) (2023)
- [Streaming data preprocessing via online tensor recovery for large environmental sensor networks](https://mlsanity.com/paper/2109.00596/) (2021)
- [Riemannian classification of EEG signals with missing values](https://mlsanity.com/paper/2110.10011/) (2021)
- [A Robust and Flexible EM Algorithm for Mixtures of Elliptical Distributions with Missing Data](https://mlsanity.com/paper/2201.12020/) (2022)
- [Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approaches](https://mlsanity.com/paper/2506.01696/) (2025)
- [T-Rex: Fitting a Robust Factor Model via Expectation-Maximization](https://mlsanity.com/paper/2505.12117/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Precise sample covariance spectral norm error -- an RDT view](https://mlsanity.com/paper/2607.14460/) (2026)

## Abstract (arXiv)

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.