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2 messages · Andrew C. Ward, Spencer Graves

Andrew C. Ward
# 
What about trying a sub-set of the data?

Regards,

Andrew C. Ward

CAPE Centre
Department of Chemical Engineering
The University of Queensland
Brisbane Qld 4072 Australia
andreww at cheque.uq.edu.au



On Saturday, April 26, 2003 10:44 AM, array chip
[SMTP:arrayprofile at yahoo.com] wrote:
Spencer Graves
# 
I think you can get what you want with the "svd" or "La.svd".  Consider 
the following:

	  The singular value decomposition ("svd" or "La.svd" in R 1.6.2) is 
something like the following:  Any n x m matrix A can be written in the 
following format:

	 A = P Lam Q,

where P and Q are orthogonal, and Lam ia diagonal.  If n < m, then we 
can consider P to be n x n, so P'P = PP' = I, Lam = n x n diagonal, and 
Q = n x m with QQ' = I.

	  Now suppose A = your data matrix minus the column means.  Then the 
sample covariance matrix, Var.A, can be written as follows:

	Var.A = AA'/(n-1) = P Lam^2 P' / (n-1).

P gives the principle components and Q the corresponding loadings or 
vice versa, I forget which now, and Lam^2/(n-1) are their associated 
variances.

If you have trouble with the details, please let us know.

hope this helps. spencer graves
Andrew C. Ward wrote: