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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) |

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? Are they in "score"?
Again, by computing PCs by eigenval decomposition:
[V,D]=eig(cov(Xm));
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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**Principal component analysis by several decomposition**,
*onewayenzyme* **<=**