Re: ? K-L decomp., PCA, POD and SVD

Am 21.09.2006 03:08 schrieb Cheng Cosine:
Hi:

What are the differences between the Karhunen-Loewe decomposition,

principle component analysis (PCA), proper orthogonal decomposition (POD)

and singular value decomposition (SVD)?

They were developed in different research areas, K-L Decomp. and PCA

were from more statistical related areas and POD and SVD were from

deterministic areas. In terms of calculations, PCA and POD could both use

SVD during determining principle vectors or proper eigen vectors.
Originally,

K-L was developed for continuous stochastic variables and PCA was for
discrete

stochastic variables. But there are also extension of K-L for discrete
variables.

POD works both for continuous and discrete deterministic variables, but SVD

works only for discrete variables.

Whatelse? When will those be identical and when will they be different?

SVD and PCA ("princi_pal_" components)/eigenvectors are identical if the
matrix to decompose is symmetric.
Don't know about the others.

Gottfried Helms
.