% TRAIN_KPCA_DENOIS Training of kernel PCA model for image denoising.
%
% Description:
% The kernel PCA model is trained to describe an input
% class of images corrupted by noise [Mika99b]. The training
% data contains images corrupted by noise and corresponding
% ground truth. The free paramaters of the kernel PCA
% are tuned by cross-validation. The objective function
% is a sum of squared differences between ground truth
% images and reconstructed images. The greedy KPCA algorithm
% is used to train the kernel PCA model.
%
% See also
% GREEDYKPCA, KPCAREC, KPCA.
%
% About: Statistical Pattern Recognition Toolbox
% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac
% <a href="http://www.cvut.cz">Czech Technical University Prague</a>
% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>
% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>
% Modifications:
% 07-jun-2004, VF
% 06-jun-2004, VF
% 17-mar-2004, VF
options.ker = 'rbf';
options.m = 500;
options.p = 10;
options.verb = 1;
num_folds = 1;
KPCA_Algo = 'greedykpca';
New_Dim_Range = [1 2];
Arg_Range = [0.5 1 2 3];
input_data_file = 'noisy_circle';
output_data_file = [];
load(input_data_file,'trn','tst');
[dim,num_data] = size(trn.X);
[itrn,itst] = crossval(num_data,num_folds);
Mse = [];
for arg = Arg_Range,
for new_dim = New_Dim_Range,
fprintf('\nnew_dim = %d, arg = %f\n', new_dim, arg);
cv_mse = 0;
for i=1:num_folds,
fprintf('\n');
trn_X = trn.gnd_X(:,itrn{i});
val_gnd_X = trn.gnd_X(:,itst{i});
val_corr_X = trn.X(:,itst{i});
fprintf('Computing Kernel PCA...');
options.arg = arg;
options.new_dim = new_dim;
kpca_model = feval( KPCA_Algo, trn_X, options);
fprintf('done.\n');
val_reconst_X = kpcarec(val_corr_X, kpca_model);
dummy = (val_reconst_X - val_gnd_X).^2;
mse = sum(dummy(:))/size(val_gnd_X,2);
fprintf('folder %d/%d: validation errors mse=%f\n', ...
i, num_folds, mse);
cv_mse = cv_mse + mse;
end
cv_mse = cv_mse/num_folds;
Mse(find(new_dim==New_Dim_Range),find(arg==Arg_Range)) = cv_mse;
fprintf('Kernel arg = %f: mse = %f\n', arg, cv_mse);
end
end
[inx1,inx2] = find(Mse==min(Mse(:)));
fprintf('\nMin(mse) = %f, dim = %f, arg = %f\n', ...
Mse(inx1,inx2), New_Dim_Range(inx1), Arg_Range(inx2) );
fprintf('Computing optimal Kernel PCA...');
options.arg = Arg_Range(inx2);
options.new_dim = New_Dim_Range(inx1);
kpca_model = feval( KPCA_Algo, trn.X, options);
fprintf('done.\n');
if isempty(output_data_file),
figure; hold on;
xlabel('\sigma'); ylabel('mse');
h = [];
clear Str;
for i=1:length(New_Dim_Range),
h = [h, plot(Arg_Range, Mse(i,:),marker_color(i) )];
Str{i} = sprintf('dim = %d', New_Dim_Range(i));
end
legend(h,Str);
else
save(output_data_file,'Arg_Range','New_Dim_Range',...
'options','Mse','num_folds','input_data_file',...
'output_data_file','KPCA_Algo','kpca_model');
end
if dim == 2 & isempty(output_data_file),
X = kpcarec(tst.X,kpca_model);
mse = sum(sum((X-tst.gnd_X).^2 ));
fprintf('\ntest mse=%f\n', mse);
figure; hold on;
h0=ppatterns(tst.gnd_X,'r+');
h1=ppatterns(tst.X,'gx');
h2=ppatterns(X,'bo');
legend([h0 h1 h2],'Ground truth','Noisy','Reconst');
end