%PREX_LOGDENS PRTools example on density based classifier improvement
%
% This example shows the use and results of LOGDENS for improving
% the classification in the tail of the distributions
%
% Note that the use of CLASSC now includes the use of logaritmic densities
% in the tails of distributions. There is no need anymore to call LOGDENS
% explicitely.
help prex_logdens
delfigs
figure
echo on
% Generate a small two-class problem
randreset(7);
a = gendatb([20 20]);
% Compute two classifiers: Mixture of Gaussians and Parzen
w_mogc = mogc(a)*classc; w_mogc = setname(w_mogc,'MoG');
w_parz = parzenc(a)*classc; w_parz = setname(w_parz,'Parzen');
% Scatterplot with MoG classifier
subplot(3,2,1);
scatterd(a);
plotc(w_mogc); xlabel(''); ylabel('');
set(gca,'xtick',[],'ytick',[])
title('MoG density classifier','fontsize',12)
drawnow
% Scatterplot with Parzen classifier
subplot(3,2,2);
scatterd(a);
plotc(w_parz); xlabel(''); ylabel('');
set(gca,'xtick',[],'ytick',[])
title('Parzen density classifier','fontsize',12)
drawnow
% Scatterplot from a distance :
% far away points are inaccurately classified
subplot(3,2,3);
%scatterd([a; [150 100]; [-150 -100]]);
scatterd([a; [75 50]; [-75 -50]]);
plotc(w_mogc); xlabel(''); ylabel('');
set(gca,'xtick',[],'ytick',[])
title('MoG: bad for remote points','fontsize',12)
drawnow
% Scatterplot from a distance :
% far away points are inaccurately classified
subplot(3,2,4);
scatterd([a; [20 12]; [-20 -12]]);
plotc(w_parz); xlabel(''); ylabel('');
set(gca,'xtick',[],'ytick',[])
title('Parzen: bad for remote points','fontsize',12)
drawnow
% Improvement of MOGC by LOGDENS
subplot(3,2,5);
%scatterd([a; [150 100]; [-150 -100]]);
scatterd([a; [75 50]; [-75 -50]]);
plotc({w_mogc,logdens(w_mogc)},['k--';'r- ']); legend off
xlabel(''); ylabel(''); set(gca,'xtick',[],'ytick',[])
title('MoG improved by Log-densities','fontsize',12)
drawnow
% Improvement of PARZEN by LOGDENS
subplot(3,2,6);
scatterd([a; [20 12]; [-20 -12]]);
plotc({w_parz,logdens(w_parz)},['k--';'r- ']); legend off
xlabel(''); ylabel(''); set(gca,'xtick',[],'ytick',[])
title('Parzen improved by Log-densities','fontsize',12)
echo off
disp(' ')
disp(' This example shows the use of the logdens() routine. It')
disp(' improves the classification in the tails of the distribution,')
disp(' which is especially important in high-dimensional spaces.')
disp(' To this end it is combined with normalisation, generating')
disp(' posterior probabilities. Logdens() can only be applied to')
disp(' classifiers based on normal densities and Parzen estimates.')
disp(' ')
showfigs