%% ct_kmeans Centroid-based clustering
% 
% <http://37steps.com/prtools/ PRTools> and <http://37steps.com/clustertools/ 
% ClusterTools> should be in the path.
%
% Goto <http://37steps.com/clustertools/clustertools-examples/ 
% ClusterTools examples> for a review of all examples.
% 
% <http://37steps.com/exam_ct/ct_kmeans/ct_kmeans.m Download the m-file from here>.
%

%% Prepare environment
prtime(10)                   % restrict iterative optimisation to 10s
delfigs                      % delete existing figures
randreset      ;             % takes care of reproducability
prwarning(2)                 % show warnings

%% Define a dataset
% we use some standard routines to create 8 two-dimensional clusters. They
% are labeld to compare cluster results with the desired labeling.A

m = 1000;
a = gendatclust2(m);
scattern(a); axis equal
title(getname(a));

%% Run two clustering procedures after removing the label information. 

x = +a; % remove labels
K = [2 3 5 8 12 20 30 50 100]; % desired cluster sizes
procs = {'KMeans','KCentres'};
err_I = cell(1,2);
err_II= cell(1,2);
figure;
for i=1:2
  subplot(2,2,i);  
  lab = x*clustk(K,procs{i});  % execute KMeans or KCentres
  scatn(lab(:,4),x,procs{i});  % scatterplot
  markcols(1);                 % show distinguishable colors colors
  axis equal;
  err_I{i}  = clusteval(lab,a,'actl');
  err_II{i} = clusteval(lab,a,'roc');
end

subplot(2,2,3); h1 = plote(err_I,10,'legend',procs);
subplot(2,2,4); h2 = plote(err_II,10,'legend',procs);

%% Comments
% KMeans clustering looks somewhat better in the scatterplots. The bottom
% left curves show that in comparison with the desired labels (figure 1)
% this is supported by active labeling by which entire clusters are 
% assigned to the label of their mediod or centre. (A cluster mean has no
% label, so the label of the nearest object, the cluster mediod, is used). 
%
% The bottom right figure shows the trade-off between the two types of
% errors as a function of the number of clusters. Error I is the fraction
% of object pairs that has been erroneously assigned to the same cluster.
% Error II is the fraction of object pairs that has been erroneously
% assigned to different clusters.