[R] Confused by SVD and Eigenvector Decomposition in PCA

antonio rodriguez arv at ono.com
Fri Feb 7 09:32:03 CET 2003

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.


Antonio Rodriguez

----- Original Message -----
From: "Feng Zhang" <f0z6305 at labs.tamu.edu>
To: "R-Help" <r-help at 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
> the first principal component explain the total variances among the
> 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
> 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
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