PLS

perform PLS calculation by using NIPALS algorithm.

Description

standard PLS by using NIPALS algorithm.
Inputs:
x n*m matrix
y n*l matrix

Outputs:
t n*max(m,l) matrix
p m*max(m,l) matrix
u n*max(m,l) matrix
q l*max(m,l) matrix
b max(m,l)*max(m,l) matrix

important properties:

x = t*p';
y = u*q';

ti' * tj = 0;
wi' * wj = 0;

refs:
[1] S. J. Qin, "Statistical Process Monitoring: Basics and Beyond," Journal of Chemometrics, vol. 17, pp. 480-502, 2003.
[2] P. Geladi and B. R. Kowalski, "Partial Least Squares Regression: A Tutorial," Analytica Chimica Acta, vol. 185, pp. 1-17, 1986.

• MATLAB release: MATLAB 7.4 (R2007a)

[Scott Miller]

The user should center the data before sending to the PLS routine.

Scott

[Martin P.]

How do I center the data for this PLS routine? Should I (1) subtract the mean of each column in X (and Y) from this column or (2) subtract the mean of the entire matrix from all its elements for X (and then Y)?

[Edgar Guevara Codina]

In order to be compatible with matlab 6.5 the function definition should have comma separated outputs as follows:
function [t,p,u,q,w,b] = PLSI (x,y)
instead of:
function [t p u q w b] = PLSI (x,y)
Besides that, it's a very illustrative program.

[Berlioz Berlioz]

what w is? The Weigth matrix of the PLS model?

[César Souza]

Maybe I am doing something wrong, but I could not verify the property y = u*q' .

[Stefan Krämer]

I could not verify the property y = u*q', either!