polypls.m

偏最小二乘算法在MATLAB中的实现

function [p,q,w,t,u,b,ssqdif] = polypls(x,y,lv,n)
%POLYPLS PLS regression with polynomial inner-relation.
%  The inputs are the matrix of predictor variables (x),
%  the vector or matrix of the predicted variable (y),
%  the maximum number of latent variables to consider (lv)
%  and the order of the polynomial for the inner-relation (n).
%  The outputs are the x-block loadings (p), the y-block 
%  loadings (q), the x-block weights (w), the x-block scores (t),
%  the y-block scores (u), the matrix of inner-relation
%  coefficients (b) and the variance explained (ssq).
%  Use POLYPRED to make predictions with new data.
%  I/O format is: [p,q,w,t,u,b,ssqdif] = polypls(x,y,lv,n);

%  Copyright
%  Barry M. Wise
%  1991
%  Modified by B.M. Wise, November 1993

[mx,nx] = size(x);
[my,ny] = size(y);
p = zeros(nx,lv);
q = zeros(ny,lv);
w = zeros(nx,lv);
t = zeros(mx,lv);
u = zeros(my,lv);
b = zeros(n+1,lv);
ssq = zeros(lv,2);
ssqx = sum(sum(x.^2)');
ssqy = sum(sum(y.^2)');
for i = 1:lv
  [pp,qq,ww,tt,uu] = plsnipal(x,y);
  b(:,i) = (polyfit(tt,uu,n))';
  x = x - tt*pp';
  y = y - (polyval(b(:,i),tt))*qq';
  ssq(i,1) = (sum(sum(x.^2)'))*100/ssqx;
  ssq(i,2) = (sum(sum(y.^2)'))*100/ssqy;
  t(:,i) = tt(:,1);
  u(:,i) = uu(:,1);
  p(:,i) = pp(:,1);
  w(:,i) = ww(:,1);
  q(:,i) = qq(:,1);
end
ssqdif = zeros(lv,2);
ssqdif(1,1) = 100 - ssq(1,1);
ssqdif(1,2) = 100 - ssq(1,2);
for i = 2:lv
  for j = 1:2
    ssqdif(i,j) = -ssq(i,j) + ssq(i-1,j);
  end
end
disp('  ')
disp('        Percent Variance Captured by PLS Model')
disp('  ')
disp('             ----X-Block------   ----Y-Block------')
disp('      LV#    This LV    Total    This LV    Total ')
disp([(1:lv)' ssqdif(:,1) cumsum(ssqdif(:,1)) ssqdif(:,2) cumsum(ssqdif(:,2))])