Re: Help on Partial Least Squares Aalgorithm

From: Hiu Chung Law (antispam_at_antispam.org)
Date: 02/16/05 

Date: 16 Feb 2005 16:23:30 GMT

Paige Miller <paige.miller@kodak.com> wrote:
> 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

As a side note, I have encountered different versions of partial
least square when I google on the web.
Do you have any references that discuss the various variants of
partial least square?

Thank you.

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