This paper investigates the robust linear discriminant analysis (LDA) problem with elliptical distributions in high-dimensional data. We propose a robust classification method, named SSLDA, that is intended to withstand heavy-tailed distributions. We demonstrate that SSLDA achieves an optimal convergence rate in terms of both misclassification rate and estimate error. Our theoretical results are further confirmed by extensive numerical experiments on both simulated and real datasets. Compared with current approaches, the SSLDA method offers superior improved finite sample performance and notable robustness against heavy-tailed distributions.

翻译：本文研究了高维数据中具有椭圆分布的鲁棒线性判别分析问题。我们提出了一种名为SSLDA的鲁棒分类方法，旨在抵御重尾分布的影响。我们证明了SSLDA在误分类率和估计误差方面均能达到最优收敛速率。我们的理论结果通过大量模拟和真实数据集的数值实验得到了进一步验证。与现有方法相比，SSLDA方法在有限样本性能上表现出显著提升，并对重尾分布具有突出的鲁棒性。