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.

翻译：二次判别分析（QDA）是一种广泛用于分类问题的方法，尤其适用于异质数据，通常优于线性判别分析（LDA）。然而，在高维设置中，当数据维度和样本量趋于无穷时，QDA会失去其有效性。为解决这一问题，我们提出了一种利用谱校正和正则化技术的新型QDA方法，称为SR-QDA。我们方法中的正则化参数通过最大化Fisher判别比来选择。我们将SR-QDA与QDA、正则化二次判别分析（R-QDA）以及其他几种竞争方法进行了比较。结果表明，SR-QDA表现优异，尤其是在中高维情况下。跨多个数据集的实证实验进一步支持了这一结论。