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

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.