Reference : Cellwise Robust regularized discriminant analysis
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Cellwise Robust regularized discriminant analysis
Aerts, Stéphanie mailto [Université de Liège > HEC Liège : UER > UER Opérations : Informatique de gestion >]
Wilms, Ines [Katholieke Universiteit Leuven - KUL > Faculty of Economics and Business > Leuven Statistics Research Centre (LStat) > >]
Statistical Analysis and Data Mining
[en] Cellwise robust precision matrix ; Classification ; Discriminant analysis ; Penalized estimation
[en] Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in high-dimension and cover the path between the two extremes QDA and LDA have been proposed in the literature. However, these procedures rely on sample covariance matrices. As such, they become inappropriate in presence of cellwise outliers, a type of outliers that is very likely to occur in high-dimensional datasets.
In this paper, we propose cellwise robust counterparts of these regularized discriminant techniques by inserting cellwise robust covariance matrices. Our methodology results in a family of discriminant methods that (i) are robust against outlying cells, (ii) cover the gap between LDA and QDA and (iii) are computable in high-dimension. The good performance of the new methods is illustrated through simulated and real data examples. As a by-product, visual tools are provided for the detection of outliers.
FWO (Research Foundation Flanders, contract number 12M8217N).
Researchers ; Professionals

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