Spectrally-Corrected and Regularized LDA for Spiked Model

Abstract

This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This approach incorporates design principles from both the spectrally-corrected covariance matrix and the regularized discriminant analysis. With the support of a large-dimensional random matrix theory, it is demonstrated that SRLDA achieves a globally optimal linear classification solution under the spiked model assumption. According to simulation data analysis, the SRLDA classifier exhibits better performance compared to RLDA and ILDA, closely to the theoretical classifier. Empirical experiments across diverse datasets further reflect that the SRLDA algorithm excels in both classification accuracy and dimensionality reduction, outperforming currently employed tools.