FEMDA: a unified framework for discriminant analysis
Pierre Houdouin Matthieu Jonckheere Frederic Pascal
Although linear and quadratic discriminant analysis are widely recognized
classical methods, they can encounter significant challenges when dealing with
non-Gaussian distributions or contaminated datasets. This is primarily due to
their reliance on the Gaussian assumption, which lacks robustness. We first
explain and review the classical methods to address this limitation and then
present a novel approach that overcomes these issues. In this new approach, the
model considered is an arbitrary Elliptically Symmetrical (ES) distribution per
cluster with its own arbitrary scale parameter. This flexible model allows for
potentially diverse and independent samples that may not follow identical
distributions. By deriving a new decision rule, we demonstrate that
maximum-likelihood parameter estimation and classification are simple,
efficient, and robust compared to state-of-the-art methods.