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rpca
Thorsten Wagner
Thorsten Wagner

Reputation: 41

Principal component analysis in R with prcomp: Reduced number of dimensions after rotation

I have a dataset with 900 examples and 3600 variables (See example #1). I did a PCA using prcomp (See example #3). Then I rotate it by #3.

data <- as.data.frame(replicate(3600, rnorm(900))); #1
pca <- prcomp(data, center = TRUE, scale. = TRUE) ;  #2
rot <- as.matrix(data) %*% pca$rotation; #3

Now the dimension of rot is 900x900, but it should be 900x3600. Why does this happen?

Best, Thosten

Upvotes: 1

Views: 1035

Answers (2)

Thorsten Wagner
Thorsten Wagner

Reputation: 41

I simply had to add more examples than variables and everything works fine. princomp() is actually forces to user to do this but prcomp() not.

Best, Thorsten

Upvotes: 0

desc
desc

Reputation: 1210

It looks like %*% makes the matrices "conformable" based on the row numbers of the first matrix given:

Multiplies two matrices, if they are conformable. If one argument is a vector, it will be coerced to a either a row or column matrix to make the two arguments conformable.

For example:

dim(as.matrix(data) %*% pca$rotation) # 900 x 900
dim(pca$rotation %*% as.matrix(data)) # 3600 x 3600

You could use transpose (or something similar) to give them the same dimensions:

rot <- as.matrix(data) %*% t(pca$rotation);

Upvotes: 1

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