Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model

• URL: http://arxiv.org/abs/2503.13582v1
• Date: Mon, 17 Mar 2025 17:21:03 GMT
• Title: Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model
• Authors: Wenya Luo, Hua Li, Zhidong Bai, Zhijun Liu,
• Abstract summary: Quadratic discriminant analysis (QDA) is a widely used method for classification problems.<n>We propose a novel QDA method utilizing spectral correction and regularization techniques, termed SR-QDA.<n>The results indicate that SR-QDA performs exceptionally well, especially in moderate and high-dimensional situations.
• Score: 5.7070383874412745
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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