TableOfReal: To Configuration (pca)...


Calculates a Configuration based on the principal components from the selected TableOfReal.
Setting

Number of dimensions

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.

1. Make the singular value decomposition of M. This results in M = U·d·V′.

2. Sort singular values d and corresponding row vectors in V (descending).

3. The principalComponent_{ij} = ∑_{k=1..numberOfColumns} M_{ik} · V_{jk}.
Remark
The resulting configuration is unique up to reflections along the new principal directions.
Links to this page
© djmw, September 9, 1998