arXiv:2604.25664stat.MLcs.LG2026-04

提出无降维的稀疏判别分析方法,提升高维数据分类准确性。

Deflation-Free Optimal Scoring

论文配图:Deflation-Free Optimal Scoring
图 1 · 摘自论文原文
  • 同时优化所有判别向量,避免逐个计算带来的误差累积。
  • 在合成与真实时间序列数据上分类精度优于传统方法。
  • 适合高维数据特征选择,尤其适用于样本少于特征的情况。

稀疏最优评分(SOS)通过弹性网络正则化重构线性判别分析,实现特征选择,适用于特征数超过样本数的高维场景。现有SOS方法多采用逐次降维策略,易产生误差传播并导致次优解。本文提出一种新方法——无降维稀疏最优评分(DFSOS),在显式全局正交约束下同时估计所有判别向量。DFSOS结合Bregman迭代与正交约束优化,将问题分解为可处理的子问题:评分向量、判别向量及正交性约束。在温和条件下,证明了其收敛至增广拉格朗日函数的驻点。大量实验使用合成数据与真实时间序列数据表明,DFSOS的分类性能达到或超过现有降维方法。结果表明,无降维策略为高维稀疏判别分析提供了鲁棒且高效的新框架。

原文摘要 · Abstract (English)

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.

稀疏判别高维数据优化算法

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