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We compare two different linear dimensionality reduction strategies for themultigroup classification problem: the trace ratio method and Fisher'sdiscriminant analysis. Recently, trace ratio optimization has gained inpopularity due to its computational efficiency, as well as the occasionallybetter classification results. However, a statistical understanding is stillincomplete. We study and compare the properties of the two methods. Then, wepropose a robust version of the trace ratio method, to handle the presence ofoutliers in the data. We reinterpret an asymptotic perturbation bound for thesolution to the trace ratio, in a contamination setting. Finally, we comparethe performance of the trace ratio method and Fisher's discriminant analysis onboth synthetic and real datasets, using classical and robust estimators.

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