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Principal component analysis by several decomposition

From: onewayenzyme
Subject: Principal component analysis by several decomposition
Date: Mon, 10 May 2021 09:45:36 -0500 (CDT)

   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


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

Again, by computing PCs by eigenval decomposition:


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

Thank you in advance

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