FEMDA: Une m\'ethode de classification robuste et flexible

TL;DR

FEMDA introduces a robust and flexible discriminant analysis method that handles heterogeneous, non-Gaussian, and contaminated datasets by modeling each data point with its own elliptical distribution and scale, improving robustness and speed.

Contribution

The paper proposes FEMDA, a novel discriminant analysis approach that accommodates heterogeneity and non-Gaussianity, enhancing robustness over traditional LDA and QDA.

Findings

FEMDA is simple and fast to compute.

It outperforms state-of-the-art methods in robustness to scale changes.

Effective on heterogeneous and contaminated datasets.

Abstract

Linear and Quadratic Discriminant Analysis (LDA and QDA) are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. This paper studies the robustness to scale changes in the data of a new discriminant analysis technique where each data point is drawn by its own arbitrary Elliptically Symmetrical (ES) distribution and its own arbitrary scale parameter. Such a model allows for possibly very heterogeneous, independent but non-identically distributed samples. The new decision rule derived is simple, fast, and robust to scale changes in the data compared to other state-of-the-art method