[실무 프로젝트로 배우는...] 주성분 분석

> ### 4.2 중고차 특성의 차원 축소를 위한 데이터 분석 기법
> 
> # 상관행렬 그래프
> # 주성분분석은 예측자들의 공분산을 활용하기 때문에 일반적으로 상관계수가 높을수록 결과가 깔끔하게 나온다.
> 
> library(corrplot)
> Corr_mat = cor(Audi2)
> corrplot(Corr_mat, method = "color", outline = T, addgrid.col = "darkgray",
+          order="hclust", addrect = 4, rect.col = "black",
+          rect.lwd = 5,cl.pos = "b", tl.col = "indianred4",
+          tl.cex = 0.5, cl.cex = 0.5, addCoef.col = "white",
+          number.digits = 2, number.cex = 0.8,
+          col = colorRampPalette(c("darkred","white","midnightblue"))(100))

> 
> # 주성분 분석
> 
> library(FactoMineR)
> Audi3 = as.data.frame(Audi2[1:100,])
> Principal_Component = PCA(Audi3,graph = FALSE)
> Principal_Component$eig
          eigenvalue percentage of variance cumulative percentage of variance
comp 1  3.483151e+00           3.483151e+01                          34.83151
comp 2  3.142647e+00           3.142647e+01                          66.25798
comp 3  1.412029e+00           1.412029e+01                          80.37827
comp 4  6.901200e-01           6.901200e+00                          87.27947
comp 5  4.931755e-01           4.931755e+00                          92.21122
comp 6  4.046871e-01           4.046871e+00                          96.25809
comp 7  2.256980e-01           2.256980e+00                          98.51507
comp 8  1.107700e-01           1.107700e+00                          99.62277
comp 9  3.772260e-02           3.772260e-01                         100.00000
comp 10 6.762775e-31           6.762775e-30                         100.00000
> # 새로 생성된 축에 대한 정보를 출력한다.
> # eigenvalue : 고유값으로 생성된 주성분 중 몇 개의 주성분을 활용할지에 대한 지표로 활용
> # percentage of variance : 생성된 주성분이 원래 예측자들을 설명하는 비율
> # cumulative percentage of variance : 주성분의 누적 변동 설명 비율
> # 제 3성분까지의 누적 설명 비율은 80.37%이다.

> 

> # Scree plot
> fviz_eig(Principal_Component, addlabels = TRUE, ylim = c(0, 50)) 

> # 주성분3까지 설명 비율이 큰 폭으로 감소한다.
> 
> # 선형결합 확인
> Principal_Component$var$coord
                             Dim.1      Dim.2       Dim.3       Dim.4       Dim.5
year                   -0.41574569  0.4316897  0.65093358 -0.16403297  0.23409851
price                   0.09959656  0.8454775  0.38541974  0.07313092 -0.19785289
mileage                 0.52823573 -0.4565412 -0.43378509  0.29998631  0.15495828
tax                     0.04476006  0.7801718 -0.08145093  0.34937178  0.45062570
mpg                     0.22433848 -0.7936643  0.31141865 -0.34671982  0.17852058
engineSize              0.80207744  0.2236029  0.21136633  0.20587087 -0.33543542
transmission_Manual    -0.61848601 -0.6161008  0.28087492  0.36274893 -0.02248080
transmission_Automatic  0.66283044  0.5013661 -0.37850451 -0.37350828  0.07528931
fuelType_Petrol        -0.86712907  0.2382348 -0.37493210 -0.07784599 -0.10390288
fuelType_Diesel         0.86712907 -0.2382348  0.37493210  0.07784599  0.10390288
> # 주성분 선형결합의 해석에서 부호(+/-)는 크게 중요하지 않고 절대값의 크기가 중요하다.
> 
> # 주성분 선형결합 시각화
> fviz_pca_var(Principal_Component, col.var="contrib",
+              gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
+              repel = TRUE # Avoid text overlapping
+ )

> fviz_pca_biplot(Principal_Component, repel = FALSE)

> # 같은 방향일수록 예측치의 상관성이 높은 것을 의미한다.

 

 

 

 

 

출처 : 실무 프로젝트로 배우는 데이터 분석 with R