Cellwise robust regularized discriminant analysis

TL;DR

This paper introduces cellwise robust regularized discriminant analysis methods that are effective in high-dimensional settings with outliers, bridging LDA and QDA while maintaining computational feasibility.

Contribution

It proposes novel cellwise robust covariance matrices integrated into regularized discriminant analysis, enhancing robustness and applicability in high-dimensional outlier-prone data.

Findings

Methods perform well on simulated data

Effective outlier detection tools are provided

Robust methods outperform traditional approaches in contaminated data

Abstract

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.