# [R] Confused by SVD and Eigenvector Decomposition in PCA

Liaw, Andy andy_liaw at merck.com
Thu Feb 6 20:14:03 CET 2003

```If I'm not mistaken, for positive semi-definite matrices, the eigenvalues
are equal to squared singular values, so you should get the same answer
either way.

The code you shown is definitely not R (looks like Matlab), so why are you
posting to R-help?

Andy

> -----Original Message-----
> From: Feng Zhang [mailto:f0z6305 at labs.tamu.edu]
> Sent: Thursday, February 06, 2003 1:03 PM
> To: R-Help
> Subject: [R] Confused by SVD and Eigenvector Decomposition in PCA
>
>
> Hey, All
>
> In principal component analysis (PCA), we want to know how
> many percentage
> the first principal component explain the total variances
> among the data.
>
> Assume the data matrix X is zero-meaned, and
> I used the following procedures:
> C = covriance(X) %% calculate the covariance matrix;
> [EVector,EValues]=eig(C) %%
> L = diag(EValues) %%L is a column vector with eigenvalues as
> the elements
> percent = L(1)/sum(L);
>
>
> Others argue using Sigular Value Decomposition(SVD) to
> calculate the same quantity, as:
> [U,S,V]=svd(X);
> L = diag(S);
> L = L.^2;
> percent = L(1)/sum(L);
>
>
> So which way is the correct method to calculate the
> percentage explained by
> the first principal component?
>
>
> Fred
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-help
>

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