%% lcurves
% Learning curves for Bayes-Normal, Nearest Mean and Nearest Neighbour 
% on the Iris dataset. Averages over 100 repetitions.
%
% <http://37steps.com/software/prtools/ PRTools> and
% <http://37steps.com/software/prdatafiles/ PRDataFiles> should be in the path
%
% <http://37steps.com/exam/lcurves/lcurves.m Download the m-file from
% here>.
% See http://37steps.com/prtools for more. 

%%        Show datasets and best classifier
delfigs
randreset(1)
a = iris;
a = setprior(a,0);
scattern(a*pcam(a,2));
title('Projection of the Iris dataset')
fontsize(14);

%%       Show learning curve of qdc with apparent error
figure
prwarning off;
e = cleval(a,qdc,[6 8 10 14  20 30 40],100);
plote(e,'nolegend')
legend('Test error','Apparent error')
title('Learning curve Bayes-normal (QDA) on Iris data')
ylabel('Averaged error (100 exp.)');
fontsize(14);
axis([2.0000 40.0000 0 0.1200])
%%
% The two curves approximate each other to the performance of the best
% possible QDA model.

%%      Show learning curves of nmc and k-nn
e2 = cleval(a,nmc,[2 3 4 5 6 8 10 14  20 30 40],100);
e3 = cleval(a,knnc,[2 3 4 5 6 8 10 14  20 30 40],100);
figure;
plote({e2,e3,e},'nolegend','noapperror')
title('Learning curves for Iris data')
ylabel('Averaged error (100 exp.)');
legend('Nearest Mean','k-Nearest Neighbor','Bayes Normal')
fontsize(14);
axis([2.0000 40.0000 0 0.1200])
%%
% For small training sets more simple classifiers are better. More
% complicated classifiers (more parameters to be estimated) are expected to
% perform better for larger training sets. The k-NN classifier improves
% slowly, but is expected to beat Bayes Normal at some point as it
% asymptotically approximates the Bayes classifier. 
%
% The learning curve for the Nearest Mean classifier shows surprisingly a
% minimum, a phenomenon 
% <http://link.springer.com/chapter/10.1007/978-3-642-34166-3_34 discussed
% by Marco Loog et al.>