%
% Example 6.7
% This shows how to use the function for the whole MBC procedure.
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; drawnow; 
rehash; 
clc; 
clear; addpath( '../../Code/eda_data' ); addpath( '../../Code/eda_toolbox' ); addpath( '../Chapter1' );

%X = load_skulls(0,0,0,0);
X = load_skulls(1,0,1,0);  % <- computation z-score 
%X = load_skulls(1,0,0,1); % <- PCA based dimensionality reduction ... 
%X = load_skulls(1,0,0,2); % <- SVD based dimensionality reduction ... 
[n,p] = size(X); data = X; 

% Do the agglomerative model-based clustering which is included in the EDA Toolbox and the MBC Toolbox.
Z = agmbclust(X);

% Construct a dendrogram.
figure; dendrogram(Z); title('Results for Skulls Data - Agglomerative MBC')
saveas( gcf, '../../WriteUp/Graphics/Chapter6/prob_6_7_skulls_dendrogram', 'epsc' ); 

% Consider the uniform-gap statistics to determine the number of clusters
% -- modified from Example 5.7
% 
K = 6; 
B = 50; 
[Z, khat, gap, Wobs, muWb] = gap_uniform(X,K,B);
fprintf('khat = %10d\n',khat); 

% from the gap-statistic plot we find a prediction of four clusters

figure; plot(1:K,Wobs,'o-',1:K,muWb,'x-')
legend({'Observed';'Expected'})
xlabel('Number of Clusters k')
ylabel('Observed and Expected log(W_k)')
%saveas( gcf, '../../WriteUp/Graphics/Chapter6/prob_6_7_skulls_wobs', 'epsc' ); 

figure; plot(1:K,gap,'o-');
xlabel('Number of Clusters k'); ylabel('Gap')
%saveas( gcf, '../../WriteUp/Graphics/Chapter6/prob_6_7_skulls_gap', 'epsc' ); 

% We can apply the silhouette procedure for this result after we find a partition. 
cind = cluster(Z,'maxclust',3);
figure; [S,H] = silhouette(X,cind);
fprintf('mean silhouette value = %10.6f\n', mean(S) ); 
title('Silhouette Plot - Agglomerative MBC')
saveas( gcf, '../../WriteUp/Graphics/Chapter6/prob_6_7_skulls_silhouette', 'epsc' );