Principal component analysis by several decomposition

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Principal component analysis by several decomposition

onewayenzyme
Hello,
   I am coping with PCA obtained after several matrix decomposition of a
data matrix containing biological information (for sake of completeness,
matrix of metabolites and samples). I have a few of doubts about the
procedure and results, then I will be greatfull to everyone who will address
some (or all) of my issues.

1. Be X a m x n data matrix (n are variables/metabolites, m
observables/samples), n is much greater than m;
2. I applied a scaling by Xm=zscore(X);
3. performed svd by [U S W]=svd(Xm);

Assuming that W contains the principal components (PCs) of Xm (is it right,
or I have to compute W'*Xm' to get them?), I can plot PCs one by one for
each sample obtaining a biplot; now, how can I get the coefficients
associated to each variables for each PCs?

In addition, it seems that a more ready procedure is to compute pca by
"princomp":

[coeff,score,latent]=princomp(Xm)

and in that case the coefficients are within the "coeff" matrix, but where
are the PCs stored?

Again, by computing PCs by eigenval decomposition:

[V,D]=eig(cov(Xm));

I will get the V'*Xm' matrix which contains the PCs, but where are the
coefficients?

Thank you in advance




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