% 
% example epage 104 
% problem epage 128 
% 
% 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; 
clc; 
clear; addpath( '../../Code/eda_data' ); addpath('../Chapter1'); 

% get some bivariate data with two well separated clusters 
% 
x1 = mvnrnd( 3*[-1,-1], [ 1, 0; 0, 1 ], 100 ); 
x2 = mvnrnd( 3*[+1,+1], [ 1, 0; 0, 1 ], 100 ); 
X = [ x1; x2 ]; data = X; 
figure; plot( X(:,1), X(:,2), 'x' ); title( 'the original data' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter5/prob_5_8_orig_data', 'epsc' ); 

y = pdist(data,'euclidean'); 

if( 0 ) 
  z = linkage(y); % <- use the default of single linkage d(S,R) = min_{i \in S,j \in R}(x_i,x_j) 
  figure; dendrogram(z); 
  title( 'single linkage' ); 
  saveas( gcf, '../../WriteUp/Graphics/Chapter5/prob_5_8_sl', 'epsc' ); 
end

% try the average distance ... considered by many to be quite good: 
% 
y = pdist(data,'euclidean'); 
z = linkage(y,'average'); 
figure; dendrogram(z); 
title( 'average linkage' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter5/prob_5_8_average', 'epsc' ); 

% Consider the uniform-gap statistics
% -- modified from Example 5.7
% 
K = 10; 
B = 100; 
link_method = 'average'; 
pdist_method = 'euclidean'; 
[Z, khat, gap, Wobs, muWb] = gap_uniform(X,K,B,link_method,pdist_method); 
fprintf('khat = %10d\n',khat); 

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/Chapter5/prob_5_8_oe', 'epsc' ); 

figure,plot(1:K,gap,'o-'),title('Gap')
xlabel('Number of Clusters k'); ylabel('Gap')
saveas( gcf, '../../WriteUp/Graphics/Chapter5/prob_5_8_gap', 'epsc' );