Pull out most important variables from PCA

Question

I would like to get the most important variables from a PCA result. I see two clusters in the plot. I now that is possible that there is no only one variable causing this, so maybe I would have to get more than one variable.

I'm using "Adegenet" R package. My original data is a matrix where rows are PubMed papers and columns are MeSH keywords. Data has been transformed into SNP-like to adapt the method to the new input data. Please point me the the correct R package if you think I'm doing the incorrect work with this package, I just chose it because I already knew how it works.

#R code
library(adegenet)
#Load SNPs
myPath <- "pubmed_result_metagenomics_ALL_parsed.fasta"#core SNPs retrieved with kSNP from 188 H. parasuis strains, removing from the analysis the strains tagged with ‘NK’ phenotype. kSNP k-mer sizes tested were 25, 20 and 15, selecting the run that gave more SNPs, i.e., 15.
core_SNPs_matrix <- fasta2genlight(myPath, chunk=1000, multicore=FALSE)#
core_SNPs_matrix <- as.matrix(core_SNPs_matrix)

# Principal Component Analysis (PCA)
pca1 <- glPca(core_SNPs_matrix) # 10 components saved
pca1

# Draw PCA colorplot
myCol <- colorplot(pca1$scores,pca1$scores, transp=TRUE, cex=4)
abline(h=0,v=0, col="grey")
add.scatter.eig(pca1$eig[1:40],2,1,2, posi="topright", inset=.05, ratio=.3)
title("First two dimensions of PCA \n based on 1359 metagenomcs papers \n and 3459 MeSH terms")
dev.copy2pdf(file = "Figure_12.pdf") #Save as .pdf#

Answer 1

The "most important" principal component is usually considered to be the one with the largest eigenvalue. If your package works in the usual way this should be the first principal component, PC1. To see how important each component is, divide the eigenvalues by the number of variables you are decomposing. This tells you the percent of the variation in the data "explained" by each component. How many components you use is ultimately up to you, though you may want to look at this paper.

EDIT To find the most important variables in terms of their contributions to the principal component, you will indeed have to look at loadings. Loadings are the projections of the principal components onto your variables. A particularly high (or particularly low) loading for a specific variable means that principal component is intimately related to the variable. My experience with PCA is mostly from stock returns, where we think of high loadings as representing some exposure for a company from an underlying risk. In this setting, high loadings mean lots of exposure. Here you could think of them as some common subject matter across papers, and the loading is how much that paper fits into that subject (or depending on how your data is organized how much the keyword fits into that subject).

So it absolutely makes sense to look at those variables which contribute most to your principal component, and to find them in terms of the absolute value of their loadings - as the meaning of a principle component is ultimately unclear.