USArrests
내장 데이터 사용
head(USArrests)
Murder Assault UrbanPop Rape Alabama 13.2 236 58 21.2 Alaska 10.0 263 48 44.5 Arizona 8.1 294 80 31.0 Arkansas 8.8 190 50 19.5 California 9.0 276 91 40.6 Colorado 7.9 204 78 38.7
분산 구하기
var(USArrests)
Murder Assault UrbanPop Rape Murder 18.970465 291.0624 4.386204 22.99141 Assault 291.062367 6945.1657 312.275102 519.26906 UrbanPop 4.386204 312.2751 209.518776 55.76808 Rape 22.991412 519.2691 55.768082 87.72916
분산만 구하기
diag(var(USArrests))
Murder Assault UrbanPop Rape 18.97047 6945.16571 209.51878 87.72916
분산 합 구하기
sum(diag(var(USArrests)))
[1] 7261.384
주성분분석 실행
arrest.pca = prcomp(USArrests)
arrest.pca
Standard deviations (1, .., p=4): [1] 83.732400 14.212402 6.489426 2.482790 Rotation (n x k) = (4 x 4): PC1 PC2 PC3 PC4 Murder 0.04170432 -0.04482166 0.07989066 -0.99492173 Assault 0.99522128 -0.05876003 -0.06756974 0.03893830 UrbanPop 0.04633575 0.97685748 -0.20054629 -0.05816914 Rape 0.07515550 0.20071807 0.97408059 0.07232502
주성분분석 요약
summary(arrest.pca)
Importance of components: PC1 PC2 PC3 PC4 Standard deviation 83.7324 14.21240 6.4894 2.48279 Proportion of Variance 0.9655 0.02782 0.0058 0.00085 Cumulative Proportion 0.9655 0.99335 0.9991 1.00000
각 차원마다 어떤 값을 가지는지 확인
arrest.pca$x
PC1 PC2 PC3 PC4 Alabama 64.802164 -11.4480074 -2.49493284 -2.4079009 Alaska 92.827450 -17.9829427 20.12657487 4.0940470 Arizona 124.068216 8.8304030 -1.68744836 4.3536852 Arkansas 18.340035 -16.7039114 0.21018936 0.5209936
시각화
biplot(arrest.pca)