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From: "Greg Heath" <heath@alumni.brown.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: negative eigenvalue in principal component analysis
Date: Sun, 4 Mar 2012 20:34:14 +0000 (UTC)
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"aymer" wrote in message <jir4ee$t1d$1@newscl01ah.mathworks.com>...
> Hello there,
> 
> I am trying to reconstruct a function using PCA. Here is what I do.
> I divide my data range into N number of bins (at first attempt 25). I assume that my function is given by some constant number over each bin, i.e f(x)=sum(beta(i)). I reconstruct my theoretical predictions using this and construct chi-squared using data values. Now to find the fisher matrix , I take a fiducial model for this unknown parameters beta,I take them all to be equal to 1 (I read somewhere that the reconstruction does not depend much on these values). Next I find out the eigenvalues and eigen vectors of this fisher matrix using eig command. The problem is some of the eigen values are coming out to be negative.
> 
> The errors in the principal components goes as 1/sqrt(eigenvalue). Is one supposed to take the magnitude of the eigenvalues???
> 
> can someone kindly suggest a solution or some references...
> thanx in advance

Negative eigenvalues with a significant magnitude indicate a serious model misspecification. You might rethink the equality assumption and/or use fewer original variables.

Negative eigenvalues with insignificant magnitudes indicate a less serious model misspecification. Typically, it just indicates the use of too many variables that are highly correlated. 

Examine the coefficents of the negative eigenvalue eigenvectors as well as the higher 
magnitude values of the correlation coefficient matrix.
 
Hope this helps.

Greg