CODEWITHSUNDEEP
rpcapredict
orrymr
orrymr

Reputation: 2493

Conflicting Results When Manually Calculating First Principal Component using prcomp

I am calculating the PCA for the iris dataset as follows:

data(iris)
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)

This is the first row of the iris dataset:

head(iris, 1)
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#1          5.1         3.5          1.4         0.2  setosa

For the first row, I can see that the value of the first principal component is -2.257141:

head(ir.pca$x, 1)
#           PC1        PC2       PC3        PC4
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751

But when I try extract the loadings:

ir.pca$rotation[, 1]
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
0.5210659   -0.2693474    0.5804131    0.5648565

and calculate the first principal component myself:

0.5210659 * 5.1  + -0.2693474 * 3.5  + 0.5804131 * 1.4 + 0.5648565 * 0.2

I get a different result of 2.64027.

Why is that?

Upvotes: 4

Views: 111

Answers (1)

AkselA
AkselA

Reputation: 8846

Scaling is the issue.

Either drop scaling in the prcomp() call

data(iris)
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)

head(ir.pca$x, 1)
           # PC1      PC2         PC3         PC4
# [1,] -5.912747 2.302033 0.007401536 0.003087706

ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
             # 1
# [1,] -5.912747

Or scale iris before you manually apply the loadings

ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)

head(ir.pca$x, 1)
           # PC1        PC2       PC3        PC4
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751

ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
          # [,1]
# [1,] -2.257141

Upvotes: 4

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