Mémoire

Abstract

This thesis presents the development of robust variants of Independent Component Analysis (ICA) aimed at addressing the challenges posed by outliers and missing data in real-world datasets. Traditional ICA methods often fail when faced with non-Gaussian, asymmetric data, or when data points are missing, leading to inaccurate signal separation and compromised analytical outcomes. To overcome these limitations, we introduce several innovations: a Minimum Covariance Determinant (MCD); rejection of outliers; iterative refinement techniques for missing data imputation; and robust objective functions that enhance the resilience of ICA to outliers. Through extensive simulations, the proposed robust ICA methods demonstrate significant improvements in performance, particularly in scenarios with high contamination or substantial missing data.