# Sparse quadratic classification rules via linear dimension reduction

arXiv: https://arxiv.org/abs/1711.04817 · HTML: https://mlsanity.com/paper/1711.04817/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2017.

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

- [Penalized Principal Component Analysis Using Smoothing](https://mlsanity.com/paper/2309.13838/) (2023)
- [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)

We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn't require estimation of precision matrices and scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparison with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of ESR1 gene in differentiating estrogen receptor status.