统计与决策2025，Vol.41Issue(19)：42-46,5.DOI:10.13546/j.cnki.tjyjc.2025.19.007
基于有效协方差矩阵估计的高维数据线性判别分析方法
Linear Discriminant Analysis Method for High-Dimensional Data Based on Efficient Covariance Matrix Estimation
摘要
Abstract
The classification of high-dimensional data largely relies on accurate covariance matrix estimation or precision matrix estimation.However,the singularity of the sample covariance matrix poses significant challenges to classification.In order to address this issue,this paper proposes an improved linear discriminant analysis method for high-dimensional data.First,a con-vex combination of the linear shrinkage estimator and the rotation-invariant estimator of the covariance matrix under the Froben-ius norm is constructed to develop a more effective covariance matrix estimation suitable for high-dimensional data.Second,the efficient covariance matrix estimation is used to update the population covariance matrix in the linear discriminant function,result-ing in an enhanced linear discriminant analysis method for high-dimensional data.Finally,the proposed method is compared with classical machine learning classification models through numerical experiments and empirical studies.The results demonstrate that the proposed method achieves higher accuracy and stronger robustness,proving its feasibility and effectiveness in handling high-dimensional data classification problems.Especially when the data dimension increases,the advantages of the proposed method become more significant.关键词
线性判别分析/协方差矩阵估计/高维数据分类/线性收缩估计/旋转不变估计Key words
linear discriminant analysis(LDA)/covariance matrix estimation/high-dimensional data classification/linear shrinkage estimation/rotation-invariant estimation分类
数理科学引用本文复制引用
吕泳瑶,张妍,刘奕彤,王国强..基于有效协方差矩阵估计的高维数据线性判别分析方法[J].统计与决策,2025,41(19):42-46,5.基金项目
国家自然科学基金资助项目(11971302 （）
12171307) （）
苏州经贸职业技术学院校级课题(YJ-ZK2407) （YJ-ZK2407）
