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PCA Covariance Matrix not correct for standardized input

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12-13-2010 11:00 AM
MattLevi
New Contributor
Hello All,

I computed a Principal Component Analysis using the Multivariate Tool in ArcInfo 9.3.  Input data were standardized by subtracting the mean and dividing by the standard deviation (Z-score) before PCA.  The resulting output covariance matrix produces values of variance (for each input band to itself) that do not  match the variance of that input band (should be ~ 1 in this case because the input bands have a standard deviation of ~1, but computed variance is approximately 0.42).  The PCA computes the covariance matrix correctly for  raw values (not standardized), but not for standardized data.  It is necessary for me to standardize the data, as input bands are on very different scales/units. 
Has anyone else had this problem?  Any ideas of how to get around this?   I am currently exploring the use of the correlation matrix instead of the covariance matrix using ERDAS.

Thanks for any help!

Regards,

Matt
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