Principal Component Analysis with R

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. There are two methods in R to perform PCA. One is princomp, another is prcomp. I think these two methods are almost same.

#Use data iris as example

> myiris <- iris[,-5]

> pca1 <- princomp (myiris)

> pca2 <- prcomp (myiris)

> pca1

Call:

princomp(x = myiris)

Standard deviations:

   Comp.1    Comp.2    Comp.3    Comp.4

2.0494032 0.4909714 0.2787259 0.1538707

 4  variables and  150 observations.

> pca2

Standard deviations:

[1] 2.0562689 0.4926162 0.2796596 0.1543862

Rotation:

                     PC1         PC2         PC3        PC4

Sepal.Length  0.36138659 -0.65658877  0.58202985  0.3154872

Sepal.Width  -0.08452251 -0.73016143 -0.59791083 -0.3197231

Petal.Length  0.85667061  0.17337266 -0.07623608 -0.4798390

Petal.Width   0.35828920  0.07548102 -0.54583143  0.7536574

#show the variables of pca result

> names (pca1)

[1] "sdev"     "loadings" "center"   "scale"    "n.obs"    "scores"   "call"   

> names (pca2)

[1] "sdev"     "rotation" "center"   "scale"    "x"      

> col <- rainbow(4, alpha=0.5)

> plot (pca1$loadings, col=col, pch=16, cex=4) # plot PCA1 and PCA2

> plot (pca2$rotation, col=col, pch=16, cex=4) # plot PCA1 and PCA2

#show loadings value

> loadings(pca1)

Loadings:

             Comp.1 Comp.2 Comp.3 Comp.4

Sepal.Length  0.361 -0.657 -0.582  0.315

Sepal.Width         -0.730  0.598 -0.320

Petal.Length  0.857  0.173        -0.480

Petal.Width   0.358         0.546  0.754

               Comp.1 Comp.2 Comp.3 Comp.4

SS loadings      1.00   1.00   1.00   1.00

Proportion Var   0.25   0.25   0.25   0.25

Cumulative Var   0.25   0.50   0.75   1.00

# show rotation value

> pca2$rotation

                     PC1         PC2         PC3        PC4

Sepal.Length  0.36138659 -0.65658877  0.58202985  0.3154872

Sepal.Width  -0.08452251 -0.73016143 -0.59791083 -0.3197231

Petal.Length  0.85667061  0.17337266 -0.07623608 -0.4798390

Petal.Width   0.35828920  0.07548102 -0.54583143  0.7536574

#also show PCA1 and PCA2

> plot (pca1$loadings[1:4, 1],pca1$loadings[1:4,2], col=col, pch=16, cex=4)

#plot PCA2 and PCA3

> plot (pca1$loadings[1:4, 2],pca1$loadings[1:4,3], col=col, pch=16, cex=4)

> plot (pca2$rotation[1:4, 2],pca2$rotation[1:4,3], col=col, pch=16, cex=4)

# plot PCA3 and PCA4

> plot (pca2$rotation[1:4, 3],pca2$rotation[1:4,4], col=col, pch=16, cex=4)

> plot (pca1$loadings[1:4, 3],pca1$loadings[1:4,4], col=col, pch=16, cex=4)

> pairs (pca1$loadings, col=col, pch=18, cex=3)

# plot all component

> pairs (pca2$rotation, col=col, pch=18, cex=3)

See almost the same.