报告题目：Structural Effect and Spectral Enhancement of High-Dimensional Regularized Linear Discriminant Analysis

时间：2025-08-30 08:40:00

地点:图书馆一楼会议室

讲座人：胡江

组织单位：数学与统计学院

主讲人学术简历：胡江，东北师范大学，数学于统计学院教授，博士生导师，入选“国家高层次人才特殊支持计划”青年拔尖人才。主要从事大维随机矩阵理论与大维统计分析研究，研究兴趣包括大维随机矩阵特征根与特征向量的极限性质、高维估计与假设检验。2012年博士毕业于东北师范大学，先后在新加坡国立大学、新加坡南洋理工大学、澳门大学、日本广岛大学、香港科技大学等学府访学。主持多项国家自然科学基金，发表SCI论文四十余篇，其中包括学科权威期刊 The Annals of Statistics、IEEE Transactions on Information Theory 等，目前担任SCI杂志 Random Matrices: Theory and Applications 主编。

观点综述：Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction,but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear insight into how data structure affects classification performance. To address this issue,we derive a non-asymptotic approximation of the misclassification rate and thus analyze the structural effect and structural adjustment strategies of RLDA.Based on this,we propose the Spectral Enhanced Discriminant Analysis (SEDA) algorithm,which optimizes the data structure by adjusting the spiked eigenvalues of the population covariance matrix. By developing anew theoretical result on eigenvectors in random matrix theory,we derive an asymptotic approximation on the misclassification rate of SEDA.The bias correction algorithm and parameter selection strategy are then obtained.Experiments on synthetic and real datasets show that SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.