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arXiv · 2503.13582

Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model

Wenya Luo·Hua Li·Zhidong Bai·Zhijun Liu
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Abstract

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.

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Wenya Luo, Hua Li, Zhidong Bai, Zhijun Liu. 2025-03-17. Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model. https://arxiv.org/abs/2503.13582

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