Fisher’s Linear Discriminant Analysis (LDA) has been widely used for linear classification, feature selection, and metrics learning in multivariate data analytics. To ensure high classification accuracy while optimally discovering predictive features from the data, this paper studied \(\mathbf {CDA}\), namely Combinatorial Discriminant Analysis that intends to combinatorially select a subset of features and assign weights to them optimally. \(\mathbf {CDA}\) extents the Truncated Rayleigh Flow algorithm (Tan et al. in J R Stat Soc: Ser B (Stat Methodol) 80(5):1057–1086, 2018) and improves LDA estimation under k-sparsity constraint. The experimental results based on the synthesized and real-world datasets demonstrate that our algorithm outperforms other LDA baselines and downstream classifiers. The empirical analysis shows that our algorithm can recover the combinatorial structure of optimal LDA with empirical consistency.

Fisher 线性判别分析 (LDA) 已广泛用于多元数据分析中的线性分类、特征选择和度量学习。为了确保较高的分类准确率，同时优化从数据中发现预测的特点，研究了\（\ mathbf {CDA} \） ，即Ç ombinatorial d iscriminant分析称，拟向组合地选择功能和分配权重的一个子集给他们最佳。\(\mathbf {CDA}\)扩展了截断瑞利流算法（Tan et al. in JR Stat Soc: Ser B (Stat Methodol) 80(5):1057–1086, 2018）并改进了k下的 LDA 估计- 稀疏约束。基于合成数据集和真实数据集的实验结果表明，我们的算法优于其他 LDA 基线和下游分类器。实证分析表明，我们的算法可以恢复具有经验一致性的最优LDA的组合结构。