Quadratic discriminant analysis (QDA) is a widely used method for classification problems, particularly preferable over Linear Discriminant Analysis (LDA) for heterogeneous data. However, QDA loses its effectiveness in high-dimensional settings, where the data dimension and sample size tend to infinity. To address this issue, we propose a novel QDA method utilizing spectral correction and regularization techniques, termed SR-QDA. The regularization parameters in our method are selected by maximizing the Fisher-discriminant ratio. We compare SR-QDA with QDA, regularized quadratic discriminant analysis (R-QDA), and several other competitors. The results indicate that SR-QDA performs exceptionally well, especially in moderate and high-dimensional situations. Empirical experiments across diverse datasets further support this conclusion.
View on arXiv@article{luo2025_2503.13582,
title={ Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model },
author={ Wenya Luo and Hua Li and Zhidong Bai and Zhijun Liu },
journal={arXiv preprint arXiv:2503.13582},
year={ 2025 }
}