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.

翻译：稀疏最优得分（Sparse Optimal Scoring，SOS）通过弹性网正则化实现特征选择，重新阐述了线性判别分析，使其特别适合特征数量超过观测值的高维场景。现有的大多数SOS方法采用基于收缩（deflation）的策略逐个计算判别向量，这种策略可能传播误差并产生次优解。我们提出了一种新方法，在显式全局正交约束下同时估计所有判别向量，称之为无收缩稀疏最优得分（Deflation-Free Sparse Optimal Scoring，DFSOS）。DFSOS将Bregman迭代与正交约束优化相结合，将问题分解为关于得分向量、判别向量和正交性强制执行的可处理子问题。我们在温和条件下证明了算法收敛到增广拉格朗日函数的平稳点。使用合成数据和真实世界时间序列数据的大量实验表明，DFSOS实现了与现有基于收缩的方法相当或更优的分类准确率。这些结果表明，无收缩方法为高维问题中的稀疏判别分析提供了稳健有效的框架。