一个非常经典的KPCA程序

% Kernel PCA toy example for k（xy）=exp（-||x-y||^2/rbf_var） cf. Fig. 4 in 
% @article{SchSmoMue98
%   author    = “B.~{Sch\“olkopf} and A.~Smola and K.-R.~{M\“uller}“
%   title     = “Nonlinear component analysis as a kernel Eigenvalue problem“
%   journal =         {Neural Computation}
%   volume    = 10
%   issue     = 5
%   pages     = “1299 -- 1319“
%   year      = 1998}
% This file can be downloaded from http://www.kernel-machines.org.
% Last modified: 4 July 2003


% parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
rbf_var = 0.1;
xnum = 4;
ynum = 2;
max_ev = xnum*ynum;
% （extract features from the first  Eigenvectors）
x_test_num = 15;
y_test_num = 15;
cluster_pos = [-0.5 -0.2; 0 0.6; 0.5 0];
cluster_size = 30;

% generate a toy data set
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
num_clusters = size（cluster_pos1）;
train_num = num_clusters*cluster_size;
patterns = zeros（train_num 2）;
range = 1;
randn（‘seed‘ 0）;
for i=1:num_clusters
  patterns（（i-1）*cluster_size+1:i*cluster_size1） = cluster_pos（i1）+0.1*randn（cluster_size1）;
  patterns（（i-1）*cluster_size+1:i*cluster_size2） = cluster_pos（i2）+0.1*randn（cluster_size1）;
end
test_num = x_test_num*y_test_num;
x_range = -range:（2*range/（x_test_num - 1））:range;
y_offset = 0.5;
y_range = -range+ y_offset:（2*range/（y_test_num - 1））:range+ y_offset;
[xs ys] = meshgrid（x_range y_range）;
test_patterns（: 1） = xs（:）;
test_patterns（: 2） = ys（:）;
cov_size = train_num;  % use all patterns to compute the covariance matrix

% carry out Kernel PCA
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:cov_size
  for j=i:c