How do I extract the Eigenvectors from a PCA calculated using FactoMinerR using R?

Question

I am running a PCA on some inflation data and have performed it using the PCA() command from the FactoMineR package and also using the prcomp()command. My goal is to get the Eigenvectors from the PCA for the next step in my analysis.

The results from both models gives me the exact same eigenvalues (well almost exactly the same, PCA() give me the variance while prcomp provided the standard deviation).

With prcomp(), by using the - "results.pca"$rotation - command I can obtain the Eigenvectors. I have been through the PCA() documentation but cannot find a similar command. The PCA() provides some nifty charts which I would like to use. I don't feel comfortable using the charts from one package and the eigenvectors without verifying that they are the same, even if the eigenvalues are the same.

I'm hoping that someone else has used PCA() and can help.

I have tried using the $rotation command from prcomp()on the PCA() output but that doesn't work.

The PCA() code provides a $var$cos2 command but this really doesn't appear to be the Eigenvector.

I have also tried many variations of "results.pca"$eigenvectors and $eigvectors and $eigvec.

Answer 1

Looking at the source code, I see FactoMineR::PCA() calculates eigenvectors in this way:

get_eigenvector <- function(X, row.w = NULL, col.w = NULL, ncp = 5) {
  FactoMineR::svd.triplet(X, row.w = row.w, col.w = col.w, ncp = ncp)$V
}

So let's do this:

# generate a data frame
set.seed(123)
data <- matrix(rnorm(500), nrow = 100)

# without FactoMineR, we calculate:
extract_eigenvectors <- function(data) {
  cov_matrix <- cov(data)     # covariance matrix
  eigen_decomp <- eigen(cov_matrix) # eigen decomposition
  eigen_decomp$vectors        # eigen vectors
}


> get_eigenvector(data)
           [,1]        [,2]        [,3]       [,4]      [,5]
[1,]  0.2647256 -0.40879343 -0.44795357  0.1850123 0.7265785
[2,]  0.4752942  0.04633997  0.53461279 -0.6099339 0.3378133
[3,] -0.1401984 -0.01182653  0.68182304  0.6528303 0.2985540
[4,]  0.4416909  0.82029804 -0.20773385  0.2804336 0.1011133
[5,] -0.6994779  0.39712945 -0.07409962 -0.2981958 0.5085346
> extract_eigenvectors(data)
           [,1]        [,2]        [,3]       [,4]       [,5]
[1,]  0.3340754 -0.37179506 -0.44015049 -0.1294342 0.73462670
[2,]  0.4392949  0.07183148  0.53585130  0.6628814 0.27443015
[3,] -0.1065714 -0.01244070  0.68944688 -0.6280148 0.34459853
[4,]  0.3930300  0.86093470 -0.19199830 -0.2398251 0.09969675
[5,] -0.7277249  0.33947804 -0.08325006  0.3031772 0.50628462

There are slight differences between normal way to calculate eigenvectors and how FactoMineR calculates it using the svd.triplet function.