**From:** antonio rodriguez (*arv@ono.com*)

**Date:** Fri 07 Feb 2003 - 19:36:10 EST

**Next message:**Andrej Kveder: "[R] a question regarding s-plus libraries and R"**Previous message:**Matt Davis: "Re: [R] Importing Packages Using OS-X"**In reply to:**Feng Zhang: "[R] Confused by SVD and Eigenvector Decomposition in PCA"**Next in thread:**Feng Zhang: "Re: [R] Confused by SVD and Eigenvector Decomposition in PCA"**Reply:**Feng Zhang: "Re: [R] Confused by SVD and Eigenvector Decomposition in PCA"

Message-id: <006201c2ce83$f7e346e0$0300a8c0@ono>

Hi Feng,

AFIK SVD analysis provides a one-step method for computing all the

components of the eigen value problem, without the need to compute and

store big covariance matrices. And also the resulting decomposition is

computationally more stable and robust.

Cheers,

Antonio Rodriguez

----- Original Message -----

From: "Feng Zhang" <f0z6305@labs.tamu.edu>

To: "R-Help" <r-help@stat.math.ethz.ch>

Sent: Thursday, February 06, 2003 7:03 PM

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?
*

*>
*

*> Thanks for your advices on this.
*

*>
*

*> Fred
*

*>
*

*> ______________________________________________
*

*> R-help@stat.math.ethz.ch mailing list
*

*> http://www.stat.math.ethz.ch/mailman/listinfo/r-help
*

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**Next message:**Andrej Kveder: "[R] a question regarding s-plus libraries and R"**Previous message:**Matt Davis: "Re: [R] Importing Packages Using OS-X"**In reply to:**Feng Zhang: "[R] Confused by SVD and Eigenvector Decomposition in PCA"**Next in thread:**Feng Zhang: "Re: [R] Confused by SVD and Eigenvector Decomposition in PCA"**Reply:**Feng Zhang: "Re: [R] Confused by SVD and Eigenvector Decomposition in PCA"

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