Cellwise Robust Discriminant Analysis

2026-05-28

AI Summary

This study addresses the sensitivity of traditional discriminant analysis to cell-wise outliers and missing values, which often degrades classification performance. The authors propose a novel robust discriminant analysis framework—termed cellQDA/cellLDA—that uniquely integrates both cell-wise and case-wise robust estimation throughout the entire training and prediction pipeline. By leveraging penalized maximum likelihood estimation, the method yields a unified formulation for both linear and quadratic discriminant functions, enabling direct handling of test samples containing cell-wise anomalies and missing entries without requiring preprocessing. Extensive experiments on synthetic and real-world datasets demonstrate that the proposed approach significantly outperforms existing methods in classification accuracy while maintaining strong interpretability.

Abstract

Classical discriminant analysis (DA) is based on the mean and empirical covariance matrix of each class, both of which are sensitive to outliers in the data. In the past the focus was on casewise outliers, that is, datapoints that lie far away. But nowadays there is increasing interest in cellwise outliers, that are unexpected entries in the data matrix. Removing an entire case because it has one or a few outlying cells would lose much information. Cellwise robust methods aim to detect the outlying cells and to preserve the information in the other cells. We propose a DA method that is trained by estimating the location and covariance of each class by cellwise and casewise robust estimators, that can also handle NA's. The main novelty of our approach is in the prediction on test data, that may contain outlying cells and NA's themselves. The new robust discriminant function is derived from a novel statistical model by penalized maximum likelihood. We focus on quadratic DA, but also cover the setting of linear DA. The new cellQDA and cellLDA methods perform well in simulation. The approach is illustrated on real data, and the results are interpreted with the help of graphical displays.

Problem

• cellwise outliers
• discriminant analysis
• robust estimation
• missing data
• quadratic discriminant analysis

Innovation

• cellwise outliers
• robust discriminant analysis
• penalized maximum likelihood
• missing data
• quadratic discriminant analysis