powerpls.m

偏最小二乘算法在MATLAB中的实现

function m = powerpls(x,y,lv,powers);
%POWERPLS Continuum regression using Wise-Ricker power method
%  This function calculates regression vectors using the 
%  continuum regression method developed by Wise and Ricker
%  that is based on taking the singular values of the x-block
%  to some power and then applying conventional PLS. This 
%  method thus allows for adjustment of the balance between
%  describing the input block variance versus obtaining a 
%  correlation with the output block. The inputs are the
%  matrix of predictor variables (x), vector or matrix of
%  predicted variables (y), the maximum number of latent
%  variables to consider (lv) and the row vector of powers
%  to be considered (powers). The output is the matrix of
%  regression vectors or matrices (m) starting with 1 LV and
%  the first power. The I/O format is 
%  m = powerpls(x,y,lv,powers);
%  
%  Note: PLS = 1, high powers go towards the PCR solution, 
%  low powers towards MLR. This routine may become unstable for
%  high powers (greater than 4-8).

%  Copyright
%  Barry M. Wise
%  1991
%  Modified May 1994
[mx,nx] = size(x); 
if mx >= nx
  [u,s,v] = svd(x,0);
else
  [ut,st,vt] = svd(x',0);
  u = vt; 
  s = st'; 
  v = ut;
end
[mp,np] = size(powers);
clc
for j = 1:np
  home
  mesg = sprintf('Now working on model %g out of %g.',j,np);
  disp(mesg)
  if powers(1,j) == 1.0
    xp = x;
    scl = diag(ones(1,min([mx nx])));
  else
    xp = u*(s.^powers(1,j))*v';
    scl = diag(diag(s.^powers(1,j))./diag(s));
  end
  [P,Q,W,T,U,b,ssqdif] = pls(xp,y,lv);
  cm = cumsum(conpred(b,W,P,Q,lv));
  scores = cm*v;
  temp = scores*scl*v';
  if j == 1
    m = temp;
  else
    m = [m; temp];
  end
end