# Multi-Group Quadratic Discriminant Analysis via Projection

arXiv: https://arxiv.org/abs/2601.05415 · HTML: https://mlsanity.com/paper/2601.05415/

## 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 8 Jan 2026.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Convex Optimization Approach to High-Dimensional Sparse Quadratic Discriminant Analysis](https://mlsanity.com/paper/1912.02872/) (2019)
- [Multiclass Sparse Discriminant Analysis](https://mlsanity.com/paper/1504.05845/) (2015)
- [Neyman-Pearson Multi-class Classification via Cost-sensitive Learning](https://mlsanity.com/paper/2111.04597/) (2021)
- [Optimal variable selection in multi-group sparse discriminant analysis](https://mlsanity.com/paper/1411.6311/) (2014)
- [Optimal Feature Selection in High-Dimensional Discriminant Analysis](https://mlsanity.com/paper/1306.6557/) (2013)
- [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)
- [Simultaneous sparse estimation of canonical vectors in the p>>N setting](https://mlsanity.com/paper/1403.6095/) (2014)
- [High-Dimensional Regularized Discriminant Analysis](https://mlsanity.com/paper/1602.01182/) (2016)

## Abstract (arXiv)

Multi-group classification arises in many prediction and decision-making problems, including applications in epidemiology, genomics, finance, and image recognition. Although classification methods have advanced considerably, much of the literature focuses on binary problems, and available extensions often provide limited flexibility for multi-group settings. Recent work has extended linear discriminant analysis to multiple groups, but more general methods are still needed to handle complex structures such as nonlinear decision boundaries and group-specific covariance patterns. We develop Multi-Group Quadratic Discriminant Analysis (MGQDA), a method for multi-group classification built on quadratic discriminant analysis. MGQDA projects high-dimensional predictors onto a lower-dimensional subspace, which enables accurate classification while capturing nonlinearity and heterogeneity in group-specific covariance structures. We derive theoretical guarantees, including variable selection consistency, to support the reliability of the procedure. In simulations and a gene-expression application, MGQDA achieves competitive or improved predictive performance compared with existing methods while selecting group-specific informative variables, indicating its practical value for high-dimensional multi-group classification problems. Supplementary materials for this article are available online.