/usr/share/octave/packages/statistics-1.2.3/plsregress.m is in octave-statistics 1.2.3-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | ## Copyright (C) 2012 Fernando Damian Nieuwveldt <fdnieuwveldt@gmail.com>
##
## This program is free software; you can redistribute it and/or
## modify it under the terms of the GNU General Public License
## as published by the Free Software Foundation; either version 3
## of the License, or (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{XLOADINGS},@var{YLOADINGS},@var{XSCORES},@var{YSCORES},@var{coefficients},@var{fitted}] =} ...
## plsregress(@var{X}, @var{Y}, @var{NCOMP})
## @itemize @bullet
## @item
## @var{X}: Matrix of observations
## @item
## @var{Y}: Is a vector or matrix of responses
## @item
## @var{NCOMP}: number of components used for modelling
## @item
## @var{X} and @var{Y} will be mean centered to improve accuracy
## @end itemize
##
## @subheading References
##
## @enumerate
## @item
## SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory
## Systems (1993)
##
## @end enumerate
## @end deftypefn
## Author: Fernando Damian Nieuwveldt <fdnieuwveldt@gmail.com>
## Description: Partial least squares regression using SIMPLS algorithm
function [XLOADINGS, YLOADINGS, XSCORES, YSCORES, coefficients, fitted] = plsregress (X, Y, NCOMP)
if nargout != 6
print_usage();
end
nobs = rows (X); # Number of observations
npred = columns (X); # Number of predictor variables
nresp = columns (Y); # Number of responses
if (! isnumeric (X) || ! isnumeric (Y))
error ("plsregress:Data matrix X and reponse matrix Y must be real matrices");
elseif (nobs != rows (Y))
error ("plsregress:Number of observations for Data matrix X and Response Matrix Y must be equal");
elseif(! isscalar (NCOMP))
error ("plsregress: Third argument must be a scalar");
end
## Mean centering Data matrix
Xmeans = mean (X);
X = bsxfun (@minus, X, Xmeans);
## Mean centering responses
Ymeans = mean (Y);
Y = bsxfun (@minus, Y, Ymeans);
S = X'*Y;
R = P = V = zeros (npred, NCOMP);
T = U = zeros (nobs, NCOMP);
Q = zeros (nresp, NCOMP);
for a = 1:NCOMP
[eigvec eigval] = eig (S'*S); # Y factor weights
domindex = find (diag (eigval) == max (diag (eigval))); # get dominant eigenvector
q = eigvec(:,domindex);
r = S*q; # X block factor weights
t = X*r; # X block factor scores
t = t - mean (t);
nt = sqrt (t'*t); # compute norm
t = t/nt;
r = r/nt; # normalize
p = X'*t; # X block factor loadings
q = Y'*t; # Y block factor loadings
u = Y*q; # Y block factor scores
v = p;
## Ensure orthogonality
if a > 1
v = v - V*(V'*p);
u = u - T*(T'*u);
endif
v = v/sqrt(v'*v); # normalize orthogonal loadings
S = S - v*(v'*S); # deflate S wrt loadings
## Store data
R(:,a) = r;
T(:,a) = t;
P(:,a) = p;
Q(:,a) = q;
U(:,a) = u;
V(:,a) = v;
endfor
## Regression coefficients
B = R*Q';
fitted = bsxfun (@plus, T*Q', Ymeans); # Add mean
## Return
coefficients = B;
XSCORES = T;
XLOADINGS = P;
YSCORES = U;
YLOADINGS = Q;
projection = R;
endfunction
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