Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model
This addresses a bottleneck in classification for heterogeneous data, though it appears incremental as it builds on existing QDA methods.
The paper tackled the problem of Quadratic Discriminant Analysis (QDA) losing effectiveness in high-dimensional settings by proposing a novel method called SR-QDA that uses spectral correction and regularization, resulting in exceptional performance, especially in moderate and high-dimensional situations.
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.