# Worst-Case Linear Discriminant Analysis as Scalable Semidefinite Feasibility Problems

arXiv: https://arxiv.org/abs/1411.7450 · HTML: https://mlsanity.com/paper/1411.7450/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2014.

## Built on by (most cited first, 1 of 1)

- [A Convex formulation for linear discriminant analysis](https://mlsanity.com/paper/2503.13623/) (2025)

## Abstract (arXiv)

In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case viewpoint, which is in general more robust for classification. However, the original problem of WLDA is non-convex and difficult to optimize. In this paper, we reformulate the optimization problem of WLDA into a sequence of semidefinite feasibility problems. To efficiently solve the semidefinite feasibility problems, we design a new scalable optimization method with quasi-Newton methods and eigen-decomposition being the core components. The proposed method is orders of magnitude faster than standard interior-point based SDP solvers. Experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard LDA. Our method is also much faster and more scalable than standard interior-point SDP solvers based WLDA. The computational complexity for an SDP with m constraints and matrices of size d by d is roughly reduced from O(m3+md3+m2d2) to O(d3) (m>d in our case).