CR-WPCA:一种针对高维小样本数据集的加权主成分分析方法  

CR-WPCA:A new weighted principal component analysis method for high dimensional small sample datasets

作　　者：王文杰 姜念祖 林帅男 胡敏 赵瑞[1] WANG Wen-jie;JIANG Nian-zu;LIN Shuai-nan;HU Min;ZHAO Rui(College of Mathematics and Computer,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《白城师范学院学报》2024年第5期48-56,共9页Journal of Baicheng Normal University

基　　金：吉林省科技发展计划项目(YDZJ202201ZYTS629)。

摘　　要：主成分分析(PCA)是典型的特征提取和数据降维方法,但在高维小样本数据集的处理中,容易出现维度灾难、计算复杂度高以及过拟合等问题.针对此问题,提出了改进的CR-WPCA方法,对样本矩阵进行方差加权,使用Chebyshev矩阵作为协方差矩阵,经Householder正交化后,利用Rayleigh-Ritz过程计算特征值.对新方法进行了Monte Carlo模拟实验并在6个公共数据集上评估了CR-WPCA方法的性能.在三个自然光数据集上,通过应用CR-WPCA方法获得的重构误差平均值达到了1.160 3;在三个高光谱数据集上,结合四种分类器应用CR-WPCA方法的分类准确率平均值为0.88.Principal component analysis(PCA)is a classic method for feature extraction and data dimensionality reduction.However,it encounters issues such as the curse of dimensionality,high computational complexity,and overfitting when processing high dimensional small sample datasets.To address these challenges,this paper proposes an improved CR-WPCA method,which weights the sample matrix by variance and uses the Chebyshev matrix as the covariance matrix.After Householder orthogonalization,the Rayleigh-Ritz process is employed to compute the eigenvalues.The new method was evaluated through Monte Carlo simulation experiments and assessed on six public datasets.For three natural light datasets,the average reconstruction error obtained by applying the CR-WPCA method was 1.1603;for three hyperspectral datasets,the average classification accuracy of applying the CR-WPCA method in conjunction with four classifiers was 0.88.

关 键 词：高维小样本 主成分分析 Chebyshev矩阵 Householder正交化 Rayleigh-Ritz过程 

分 类 号：G642[文化科学—高等教育学]