# Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model

arXiv: https://arxiv.org/abs/2503.13582 · HTML: https://mlsanity.com/paper/2503.13582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Estimation of the number of spiked eigenvalues in a covariance matrix by bulk eigenvalue matching analysis](https://mlsanity.com/paper/2006.00436/) (2020)
- [Estimating Number of Factors by Adjusted Eigenvalues Thresholding](https://mlsanity.com/paper/1909.10710/) (2019)
- [A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1912.02872/) (2019)
- [A Direct Approach for Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1510.00084/) (2015)
- [Innovated interaction screening for high-dimensional nonlinear classification](https://mlsanity.com/paper/1501.01029/) (2015)
- [Sparse quadratic classification rules via linear dimension reduction](https://mlsanity.com/paper/1711.04817/) (2017)
- [Quadratic Discriminant Analysis by Projection](https://mlsanity.com/paper/2108.09005/) (2021)
- [High-Dimensional Regularized Discriminant Analysis](https://mlsanity.com/paper/1602.01182/) (2016)
- [High-Dimensional Quadratic Discriminant Analysis under Spiked Covariance Model](https://mlsanity.com/paper/2006.14325/) (2020)
- [Spectrally-Corrected and Regularized Linear Discriminant Analysis for Spiked Covariance Model](https://mlsanity.com/paper/2210.03859/) (2022)

## Abstract (arXiv)

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.