%?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:cov_size
????K（ij）?=?exp（-norm（patterns（i:）-patterns（j:））^2/rbf_var）;
????K（ji）?=?K（ij）;
??end
end
unit?=?ones（cov_size?cov_size）/cov_size;
%?centering?in?feature?space!
K_n?=?K?-?unit*K?-?K*unit?+?unit*K*unit;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[evecsevals]?=?eig（K_n）;
evals?=?real（diag（evals））;
for?i=1:cov_size
??evecs（:i）?=?evecs（:i）/（sqrt（evals（i）））;
end

%?extract?features
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%??do?not?need?the?following?here?-?only?need?test?point?features
%unit_train?=?ones（train_numcov_size）/cov_size;
%for?i=1:train_num
%??for?j=1:cov_size
%????K_train（ij）?=?exp（-norm（patterns（i:）-patterns（j:））^2/rbf_var）;
%??end
%end
%K_train_n?=?K_train?-?unit_train*K?-?K_train*unit?+?unit_train*K*unit;
%features?=?zeros（train_num?max_ev）;
%features?=?K_train_n?*?evecs（:1:max_ev）;

unit_test?=?ones（test_numcov_size）/cov_size;
K_test?=?zeros（test_numcov_size）;
for?i=1:test_num
??for?j=1:cov_size
????K_test（ij）?=?exp（-norm（test_patterns（i:）-patterns（j:））^2/rbf_var）;
??end
end
K_test_n?=?K_test?-?unit_test*K?-?K_test*unit?+?unit_test*K*unit;
test_features?=?zeros（test_num?max_ev）;
test_features?=?K_test_n?*?evecs（:1:max_ev）;

%?plot?it
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3474??2006-06-29?08:10??KPCA主要在圖像去噪聲方面有應用。此外還可以進行特征提取，降維使用\KPCA\kpca_toy.m

?????目錄??????????0??2011-09-15?23:24??KPCA主要在圖像去噪聲方面有應用。此外還可以進行特征提取，降維使用\KPCA

?????目錄??????????0??2011-09-15?23:24??KPCA主要在圖像去噪聲方面有應用。此外還可以進行特征提取，降維使用

-----------?---------??----------?-----??----

?????????????????3474????????????????????3