PCA主成分分析说明应用举例.ppt

PCA主成分分析 应用举例;例1;a=c(177,179 , 95 , 96 , 53 , 32 , -7 ,-4 , -3 ,179,419 , 245 , 131 , 181 , 127 , -2 , 1 , 4 , 95 ,245 , 302 , 60 , 109 , 142 , 4 , 4 , 11 ,96 ,131 , 60 , 153 , 102 , 42 , 4 , 3 , 2 , 53 ,181 , 109 , 102 , 137 , 96 , 4 , 5 , 6 , 32 ,127 , 142 , 42 , 96 , 128 , 2 , 2 , 8 , -7 , -2 , 4 , 4 , 4 , 2 , 34 ,31 , 33 , -4 , 1 , 4 , 3 , 5 , 2 , 31 ,39 , 39 ,-3 , 4 , 11 , 2 , 6 , 8 , 33 ,39 , 48);求方差阵S的特征值和特征向量;样本前3个主成分的系数是：;例2 学生身体各指标的主成分分析.随机抽取30名某年级中学生,测量其身高(X1)、体重(X2)、胸围(X3)和坐高(X4)。 试对中学生身体指标数据做主成分分析.;#### 用数据框形式输入数据 student-data.frame( X1=c(148, 139, 160, 149, 159, 142, 153, 150, 151, 139, 140, 161, 158, 140, 137, 152, 149, 145, 160, 156, 151, 147, 157, 147, 157, 151, 144, 141, 139, 148), X2=c(41, 34, 49, 36, 45, 31, 43, 43, 42, 31, 29, 47, 49, 33, 31, 35, 47, 35, 47, 44, 42, 38, 39, 30, 48, 36, 36, 30, 32, 38), X3=c(72, 71, 77, 67, 80, 66, 76, 77, 77, 68, 64, 78, 78, 67, 66, 73, 82, 70, 74, 78, 73, 73, 68, 65, 80, 74, 68, 67, 68, 70), X4=c(78, 76, 86, 79, 86, 76, 83, 79, 80, 74, 74, 84, 83, 77, 73, 79, 79, 77, 87, 85, 82, 78, 80, 75, 88, 80, 76, 76, 73, 78)) ; cor(student) X1 X2 X3 X4 X1 1.0000000 0.8631621 0.7321119 0.9204624 X2 0.8631621 1.0000000 0.8965058 0.8827313 X3 0.7321119 0.8965058 1.0000000 0.7828827 X4 0.9204624 0.8827313 0.7828827 1.0000000 eigen(cor(student)) $values [1] 3000$vectors [,1] [,2] [,3] [,4] [1,] -0.4969661 0.5432128 -0.4496271 0.5057471 [2,] -0.5145705 -0.2102455 -0.4623300 -0.6908436 [3,] -0.4809007 -0.7246214 0.1751765 0.4614884 [4,] -0.5069285 0.3682941 0.7439083 -0.2323433 ; #### 作主成分分析 student.pr-princomp(student, cor=TRUE) #### 并显示分析结果 summary(student.pr, loadings=TRUE) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 1.8817805 000Proportion of Variance 0.8852745 00.0198