Re: Help on Partial Least Squares Aalgorithm

From: Paige Miller (paige.miller_at_kodak.com)
Date: 02/14/05 

Date: Mon, 14 Feb 2005 10:27:46 -0500

Beorne wrote:
> The PLS algorithm (on one target variable) does regression on some
> specific subsapace
> The regression problem is:
> y = XWQ + e
> where y is a single variable target vector nx1,
> X is a data vector nxP
> W is a subspace of X of pxk dimension (with k<p)
> Q are the kx1 regression coefficents.
> T=XW is the score plot.
>
> I need the W matrix of PLS only for visualization purpose, i.e. I have
> to plot the score like a PCA.
> How can I calculate directly the subspace W? I don't want to use the
> more complex PLS algorithms (NIPALS or SIMPLS) that suppose that I have
> more than one target variables and give me the regression coefficent
> matrix Q I don't need.
>
> In short: what is the formula to calculate W from X and y? (i.e.: fr
> PCA the W space is the k-biggest eigenvalue corresponding eigenvector
> space of X'*X given X standardized)

So let's see ... you don't want to use existing, well-established
algorithms because they give you stuff you don't want, and that
extra calculation is expensive.

Now there are ways to rewrite the PLS algorithm using an eigenvector
decomposition ... but darn it all, you not only get the
eigenvectors, but other stuff you don't want like eigenvalues, and
eigenvectors for dimensions you don't want. And this method requires
even more calculations than the NIPALS or SIMPLS algorithm anyway.

I guess I can't help you. 

-- 
Paige Miller
Eastman Kodak Company
paige dot miller at kodak dot com
http://www.kodak.com
"It's nothing until I call it!" -- Bill Klem, NL Umpire
"When you get the choice to sit it out or dance, I hope you dance" 
-- Lee Ann Womack

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