On the trace ratio method and Fisher's discriminant analysis for robust multigroup classification

TL;DR

This paper compares the trace ratio method and Fisher's discriminant analysis for multigroup classification, introduces a robust version of the trace ratio method to handle outliers, and evaluates their performance on synthetic and real datasets.

Contribution

It provides a comparative analysis of two linear dimensionality reduction methods and proposes a robust trace ratio approach for improved classification in contaminated data.

Findings

Robust trace ratio method improves outlier handling.

Fisher's discriminant analysis performs well on clean data.

Performance varies depending on data contamination and estimator choice.

Abstract

We compare two different linear dimensionality reduction strategies for the multigroup classification problem: the trace ratio method and Fisher's discriminant analysis. Recently, trace ratio optimization has gained in popularity due to its computational efficiency, as well as the occasionally better classification results. However, a statistical understanding is still incomplete. We study and compare the properties of the two methods. Then, we propose a robust version of the trace ratio method, to handle the presence of outliers in the data. We reinterpret an asymptotic perturbation bound for the solution to the trace ratio, in a contamination setting. Finally, we compare the performance of the trace ratio method and Fisher's discriminant analysis on both synthetic and real datasets, using classical and robust estimators.