LDA分类模型与改进分类模型的对比分析  

Comparative analysis of LDA classification model and improved classification model

作　　者：李华[1] 刘洁 LI Hua;LIU Jie(College of Mathematics and Statistic,Changchun University,Changchun 130022,China)

机构地区：[1]长春大学数学与统计学院,吉林长春130022

出　　处：《吉林师范大学学报（自然科学版）》2024年第2期60-68,共9页Journal of Jilin Normal University:Natural Science Edition

基　　金：吉林省科技厅产业关键核心技术攻关课题(20220201160GX)。

摘　　要：考虑在协方差矩阵遵循尖峰模型的假设下,对样本协方差矩阵结构进行频谱校正,在保留大Spiked特征根的同时,增加对极小特征根的研究,以此构成的分类模型称为SC-LDA.通过实证对比得到以下结论:在不使用PCA降维的情况下,经典LDA、R-LDA、I-LDA和SC-LDA的分类误差率分别为:0.328 5、0.327 9、0.319 3、0.318 3,经过PCA算法的特征提取后的最低误分类率分别为0.320 3、0.319 0、0.313 0、0.312 0.显然,PCA算法与改进分类模型的结合,有效地提高了该模型的分类性能;同时,与其他模型相比,SC-LDA更完整地保留总体协方差矩阵的结构,其分类性能优胜于经典LDA、R-LDA和I-LDA.Under the assumption that the covariance matrix follows the peak model,the classification model is called SC-LDA by adding the study of minimal feature root.Through empirical comparison,the following conclusions can be drawn:Without PCA dimension reduction,the classification error rates of classical LDA,R-LDA,I-LDA,and SC-LDA are 0.3285,0.3279,0.3193,0.3183,and the lowest classification error rates after PCA feature extraction are 0.3203,0.3190,0.3130,0.3120,respectively.Obviously,the combination of the PCA algorithm and improved classification model can effectively improve the classification performance of the model.Meanwhile,compared with other models,SC-LDA retains the structure of the total covariance matrix more completely,and its classification performance is superior to classical LDA,R-LDA,and I-LDA.

关 键 词：线性判别分析 主成分分析 随机矩阵 频谱校正 

分 类 号：O212.5[理学—概率论与数理统计]