Robust classification with flexible discriminant analysis in heterogeneous data

2022/01/09 by Pierre Houdouin, Houdouin, Pierre, Frédéric Pascal +5
Chemistry · Engineering · Mathematics · #Spectroscopy and Chemometric Analyses #Fault Detection and Control Systems #Advanced Statistical Methods and Models

paper · pdf · doi:10.48550/arxiv.2201.02967

Abstract

Linear and Quadratic Discriminant Analysis 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. To fill this gap, this paper presents a new robust discriminant analysis 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. After deriving a new decision rule, it is shown that maximum-likelihood parameter estimation and classification are very simple, fast and robust compared to state-of-the-art methods.

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