For this, I think a nice approach is the cross validation method
discussed by Svante Wold in a Technometrics paper in the seventies
or early eighties.
At 16:15 -0400 05/04/2000, [EMAIL PROTECTED] wrote:
>Greetings,
>
>I'm hoping that you could help me resolve a problem that I have been
>working on for quite sometime.
>
>We are using PCA, Principal Components Analysis, with arbitrary large
>datasets. Thus, we are working only with correlation matrices, and
>naturally we hope that PCA will significantly reduce the
>dimensionality of our dataset. Currently we employ proportion of
>trace explained to determine which pc's to keep. However, after
>considerable reading on the subject, we discovered that this isn't the
>best route to take. Thus we have decided to look into using stopping
>rules based on how much residual variability that one is willing to
>accept. This is where confusion sets in.
>
>Now my primary source of information has been J. Edward Jackson's "A
>User's Guide to Principal Component Analysis." In this book he
>describes a number of methods to determine if an outlier exists within
>the data, using residual analysis. However, it is unclear to me how
>this factors into determining which pc's to keep, since most of the
>statistics in regard to residual analysis deal specifically with
>scores obtained from a data vector. I suspect that we can determine
>this by continually testing the diagonal of the residual matrix until
>it meats our criteria, but I'm not entirely sure. Is this a 'good'
>approach to take in determining which pc's to keep? Keep in mind that
>this needs to be determined without user intervention. I also
>understand that appropriate significance tests must be performed
>before this operation.
>
>Also, just out of curiousity, if we added a sample in principal
>component space, reduced dimensionality, and applied an inversion on
>this data element, would we get a value in original space that closely
>matched, given our residual criteria, what the actual data element
>should be. It would seem true given that we were willing to
>sacrifice so much variability performing a PCA. Thus inverting it
>would be close to the actual value but off by criteria given.
>
>Many thanks for your assistance,
>
>Jason Walter
>CSC Graduate Student
>[EMAIL PROTECTED]
>
>
>
>
>
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--
===
Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
US mail: 8142 Math Sciences Bldg, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550; fax (310)-206-5658; email: [EMAIL PROTECTED]
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