%?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