Spectrally-Corrected and Regularized Linear Discriminant Analysis for Spiked Covariance Model

TL;DR

This paper introduces SRLDA, an improved linear discriminant analysis method that leverages spectral correction and regularization, demonstrating superior classification performance in high-dimensional settings under the spiked covariance model.

Contribution

It develops a spectrally-corrected and regularized LDA with a proven optimal solution under the spiked model, enhancing classification accuracy in high-dimensional data.

Findings

SRLDA outperforms RLDA and ILDA in simulations.

SRLDA achieves results closer to the theoretical classifier.

Experiments show SRLDA improves classification and dimensionality reduction.

Abstract

This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized discriminant analysis. With the support of a large-dimensional random matrix analysis framework, it is proved that SRLDA has a linear classification global optimal solution under the spiked model assumption. According to simulation data analysis, the SRLDA classifier performs better than RLDA and ILDA and is closer to the theoretical classifier. Experiments on different data sets show that the SRLDA algorithm performs better in classification and dimensionality reduction than currently used tools.