求助：关于KPCA的matlab程序
如下2*2非线性系统，某时刻u2发生故障，用KPCA进行故障检测。谁能给点提示该如何编程~~y1(t)=2;(2为平方的意思）
y2(t)=2;(2为平方的意思）
KPCA的提出者亲自写的程序，不妨看看，或许有帮助！
:lol% Kernel PCA toy example for k(x,y)=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 <max_ev> 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_pos,1);
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_size,1) = cluster_pos(i,1)+0.1*randn(cluster_size,1);
patterns((i-1)*cluster_size+1:i*cluster_size,2) = cluster_pos(i,2)+0.1*randn(cluster_size,1);
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;
= 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(i,j) = exp(-norm(patterns(i,:)-patterns(j,:))^2/rbf_var);
K(j,i) = K(i,j);
end
end
unit = ones(cov_size, cov_size)/cov_size;
% centering in feature space!
K_n = K - unit*K - K*unit + unit*K*unit;
= 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_num,cov_size)/cov_size;
%for i=1:train_num,
%for j=1:cov_size,
% K_train(i,j) = 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_num,cov_size)/cov_size;
K_test = zeros(test_num,cov_size);
for i=1:test_num,
for j=1:cov_size,
K_test(i,j) = 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1); clf
for n = 1:max_ev,
subplot(ynum, xnum, n);
axis([-range range -range+y_offset range+y_offset]);
imag = reshape(test_features(:,n), y_test_num, x_test_num);
axis('xy')
colormap(gray);
hold on;
pcolor(x_range, y_range, imag);
shading interp
contour(x_range, y_range, imag, 9, 'b');
plot(patterns(:,1), patterns(:,2), 'r.')
text(-1,1.65,sprintf('Eigenvalue=%4.3f', evals(n)));
hold off;
end
原始文献
原始文献 Nonlinear component analysis as a kernel Eigenvalue problem可以从IEEE 数据库当中查到！ penghx 发表于 2008-10-22 15:47 static/image/common/back.gif
原始文献 Nonlinear component analysis as a kernel Eigenvalue problem
可以从IEEE 数据库当中查到！
这个运行结果出的图该如何理解啊？
我曾经把这个代码用在意大利葡萄酒数据上，发现效果不好啊 dyhkxydfbb 发表于 2012-11-27 13:03 static/image/common/back.gif
这个运行结果出的图该如何理解啊？
我曾经把这个代码用在意大利葡萄酒数据上，发现效果不好啊
KPCA所提取的各特征的物理意义很不明确，所以很难理解，这也是KPCA的最大缺陷之一
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