# Deflation-Free Optimal Scoring

arXiv: https://arxiv.org/abs/2604.25664 · HTML: https://mlsanity.com/paper/2604.25664/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 28 Apr 2026.

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

- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [Simple algorithms for optimization on Riemannian manifolds with constraints](https://mlsanity.com/paper/1901.10000/) (2019)
- [Riemannian Optimization on the Symplectic Stiefel Manifold](https://mlsanity.com/paper/2006.15226/) (2020)
- [An exact penalty approach for optimization with nonnegative orthogonality constraints](https://mlsanity.com/paper/1907.12424/) (2019)
- [Grassmannian optimization is NP-hard](https://mlsanity.com/paper/2406.19377/) (2024)
- [Stiefel optimization is NP-hard](https://mlsanity.com/paper/2507.02839/) (2025)
- [On Relatively Smooth Optimization over Riemannian Manifolds](https://mlsanity.com/paper/2508.03048/) (2025)

## Abstract (arXiv)

Sparse Optimal Scoring (SOS) reformulates linear discriminant analysis to enable feature selection through elastic net regularization, making it well-suited for high-dimensional settings where the number of features exceeds observations. Most existing SOS methods use deflation-based strategies that compute discriminant vectors sequentially, which can propagate errors and produce suboptimal solutions. We propose a novel approach that estimates all discriminant vectors simultaneously under an explicit global orthogonality constraint, which we call Deflation-Free Sparse Optimal Scoring (DFSOS). DFSOS combines Bregman iteration with orthogonality-constrained optimization, decomposing the problem into tractable subproblems for scoring vectors, discriminant vectors, and orthogonality enforcement. We establish convergence to stationary points of the augmented Lagrangian under mild conditions. Extensive experiments using synthetic data and real-world time series data demonstrate that DFSOS achieves classification accuracy comparable to or better than existing deflation-based methods. These results indicate that deflation-free approaches offer a robust and effective framework for sparse discriminant analysis in high-dimensional problems.