# Quadratic Discriminant Analysis by Projection

arXiv: https://arxiv.org/abs/2108.09005 · HTML: https://mlsanity.com/paper/2108.09005/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2021.

## Built on by (most cited first, 3 of 3)

- [An uncertainty-aware Bayesian framework for machine learning classification models: A case study in land cover classification](https://mlsanity.com/paper/2503.21510/) (2025)
- [Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model](https://mlsanity.com/paper/2503.13582/) (2025)
- [Multi-Group Quadratic Discriminant Analysis via Projection](https://mlsanity.com/paper/2601.05415/) (2026)

## Abstract (arXiv)

Discriminant analysis, including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), is a popular approach to classification problems. It is well known that LDA is suboptimal to analyze heteroscedastic data, for which QDA would be an ideal tool. However, QDA is less helpful when the number of features in a data set is moderate or high, and LDA and its variants often perform better due to their robustness against dimensionality. In this work, we introduce a new dimension reduction and classification method based on QDA. In particular, we define and estimate the optimal one-dimensional (1D) subspace for QDA, which is a novel hybrid approach to discriminant analysis. The new method can handle data heteroscedasticity with number of parameters equal to that of LDA. Therefore, it is more stable than the standard QDA and works well for data in moderate dimensions. We show an estimation consistency property of our method, and compare it with LDA, QDA, regularized discriminant analysis (RDA) and a few other competitors by simulated and real data examples.