人脸识别方法的分析与研究
附录
% Kernel PCA toy example for k(x,y)=exp(-||x-y||^2/rbf_var), cf. Fig. 4 in
% @article{SchSmoMue98,
% author = \
% title = \% journal = {Neural Computation}, % volume = 10, % issue = 5,
% pages = \% 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
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;
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人脸识别方法的分析与研究
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(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;
[evecs,evals] = 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; tatures = zeros(train_num, max_ev); tatures = 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);
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人脸识别方法的分析与研究
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
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人脸识别方法的分析与研究
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