Robust Independent Component Analysis

S. Leyder

{}^{1}

J. Raymaekers

{}^{2}

P.J. Rousseeuw

{}^{3}

T. Van Deuren

{}^{4}

and T. Verdonck

{}^{5}

${}^{1}$

Department of Mathematics, University of Antwerp, Belgium [sarah.leyder@uantwerpen.be]
${}^{2}$

Department of Mathematics, University of Antwerp, Belgium [jakob.raymaekers@uantwerpen.be]
${}^{3}$

Section of Statistics and Data Science, University of Leuven, Belgium [peter@rousseeuw.net]
${}^{4}$

Department of Mathematics, University of Antwerp, Belgium [tom.vandeuren@uantwerpen.be]
${}^{5}$

Department of Mathematics, University of Antwerp, Belgium [tim.verdonck@uantwerpen.be]

Keywords: Independent Component Analysis – Distance Correlation – Robustness

Abstract

Independent Component Analysis (ICA) aims to separate multivariate, non-Gaussian data into statistically independent components. Unlike Principal Component Analysis (PCA), which relies on second-order statistics to decorrelate data, ICA utilizes higher-order information to achieve linear unmixing of the independent components. Various ICA approaches exist, leveraging techniques based on kurtosis, joint entropy, maximum likelihood, and mutual information. However, in contrast to PCA, relatively little research has been conducted on robust ICA methods.

In this talk we propose a new method for robust ICA. It builds on the framework of Matteson and Tsay [2017], who minimize the popular dependence measure, distance correlation, to extract the independent components. However, we robustify their approach by utilizing the more robust version of distance correlation of Leyder et al. [2024], which applies a novel data transformation called biloop to increase robustness against outliers. Extensive simulation results demonstrate the good performance of this new ICA method and its resistance towards contamination.

References

Leyder et al. [2024] S. Leyder, J. Raymaekers, and P. J. Rousseeuw. Is Distance Correlation Robust? arXiv preprint arXiv:2403.03722, 2024.
Matteson and Tsay [2017] D. S. Matteson and R. S. Tsay. Independent component analysis via distance covariance. Journal of the American Statistical Association, 112(518):623–637, 2017. Taylor & Francis.