pcrg.m

偏最小二乘算法在MATLAB中的实现

function [t,p,b,ssq,eigs] = pcrg(x,y,pc)
%PCR Principal components regression for multivariate y for use by MODLGUI

%  Copyright
%  Barry M. Wise
%  1992
%  Modified by B.M. Wise, November 1993
%  Modified by B.M. Wise, May 1995

[mx,nx] = size(x);
[my,ny] = size(y);
if mx ~= my
  error('Number of samples in x- and y-blocks not equal.')
elseif pc > nx
  error('pc must be <= number of x-block variables.')
end
if nx < mx
  cov = (x'*x)/(mx-1);
  [u,s,v] = svd(cov);
  p = v(:,1:pc);
else
  cov = (x*x')/(mx-1);
  [u,s,v] = svd(cov);
  v = x'*v;
  for i = 1:pc
    v(:,i) = v(:,i)/norm(v(:,i));
  end
  p = v(:,1:pc);
end
eigs = diag(s);
t = x*p;
b = zeros(pc*ny,nx);
ssqty = zeros(pc,1);
ssqy = sum(sum(y.^2));
for i = 1:pc
  r = inv(t(:,1:i)'*t(:,1:i))*t(:,1:i)'*y;
  b(ny*(i-1)+1:ny*i,:) = (p(:,1:i)*r)';
  dif = y - t(:,1:i)*r;
  ssqty(i,1) =  ((ssqy - sum(sum(dif.^2)))/ssqy)*100;
end
temp = diag(s)*100/(sum(diag(s)));
temp = temp(1:pc);
ssqy = zeros(pc,1);
ssqy(1,1) = ssqty(1,1);
for i = 1:pc-1
  ssqy(i+1,1) = ssqty(i+1,1)-ssqty(i,1);
end
ssq = [(1:pc)' temp cumsum(temp) ssqy ssqty];