Robust classification with flexible discriminant analysis in heterogeneous data
This addresses the issue of poor performance in heterogeneous data for statisticians and data scientists, offering an incremental improvement over classical methods.
The paper tackles the problem of classification with discriminant analysis in non-Gaussian and contaminated datasets by proposing a robust method where each data point follows its own elliptical symmetrical distribution and scale parameter, resulting in a simple, fast, and robust approach compared to state-of-the-art methods.
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.