TableOfReal: To Configuration (pca)...
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Calculates a Configuration based on the principal components from the selected TableOfReal.
Setting
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Number of dimensions
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determines the number of dimensions of the resulting Configuration.
Algorithm
We form principal components without explicitly calculating the covariance matrix C = M′·M, where M is the matrix part of the TableOfReal.
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1. Make the singular value decomposition of M. This results in M = U·d·V′.
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2. Sort singular values d and corresponding row vectors in V (descending).
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3. The principalComponentij = ∑k=1..numberOfColumns Mik · Vjk.
Remark
The resulting configuration is unique up to reflections along the new principal directions.
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© djmw, September 9, 1998