针对高维数据提出改进QDA分类器，提升分类准确率
Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model
- 用谱修正与正则化改进传统QDA方法
- 在中高维场景下分类性能显著优于现有方法
- 适合处理维度远大于样本数的复杂数据
二次判别分析（QDA）广泛应用于分类问题，尤其适用于异质数据，但在高维设置下表现不佳，当数据维度与样本量趋于无穷时。为此，本文提出一种新型QDA方法——谱校正与正则化QDA（SR-QDA），通过最大化Fisher判别比来选择正则化参数。与标准QDA、正则化QDA（R-QDA）及其他竞争方法相比，实验结果表明，SR-QDA在中高维情形下表现优异。跨多种数据集的实证研究进一步验证了其有效性。
原文摘要 · Abstract (English)
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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