High Dimensional Robust Classification: A Random Matrix Analysis

This article proposes a random matrix analysis of the spectral properties of a new robust kernel matrix model adapted to elliptically distributed large dimensional data mixtures. It is shown that these kernel matrices, based on robust estimators of scatter, when finely tuned, can perform asymptotic non-trivial (unsupervised) classification while sample covariance matrices are ineffective. Unlike in conventional robust statistics wisdom though, the “maximally robust” estimators (such as Tyler's estimator of scatter) also break asymptotic classification feasibility. This entails the existence of an optimal robustness-classification trade-off which we discuss.