function chain_letter_dendrogram ( )
%*****************************************************************************80
%
%% chain_letter_dendrogram() makes a dendrogram from a distance matrix.
%
% Discussion:
%
% Students were given 11 chain letters. Each student was asked to pick
% a particular chain letter, and then estimate its "distance" from all
% the chain letters, using a particular scoring system.
%
% The results are here assembled into a distance matrix, from which a
% hierarchical clustering can be made and displayed.
%
% The distances were based on comparing positions in thw chain letters where
% a proper name occurred.
%
% "New England" 0 if the same, 1 otherwise.
% "R.A.F.Officer" 0 if the same, 1 otherwise.
% "Gene Welch" 0 if the same, 1 if one name different, 2 if both different.
% "Saul de Groda" 0 if the same, 1, 2 or 3 if 1, 2 or 3 names different or added.
% "Constantine Dias" 0 if the same, 1 or 2 if 1 or 2 names different.
% "Carlos Daddit" 0 if the same, 1 or 2 if 1 or 2 names different.
% "Dalan Fairchild" 0 if the same, 1 or 2 if 1 or 2 names different.
% "a young woman in California" 0 if both letters have or don't have this part,
% 5 if one does and one doesn't.
%
% The distance between the two chain letters is the sum of the 8 scores.
%
% From the distance matrix, we can compute a dendrogram that suggests,
% based on similarity, a sort of genealogy for the chain letters.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 02 May 2019
%
% Author:
%
% John Burkardt
%
fprintf ( 1, '\n' );
fprintf ( 1, 'chain_letter_dendrogram():\n' );
fprintf ( 1, ' MATLAB/Octave version %s:\n', version ( ) );
fprintf ( 1, ' Construct a dendrogram to analyze the relationship\n' );
fprintf ( 1, ' among a set of 11 versions of a chain letter.\n' );
%
% Read the distance matrix from a file.
%
filename = 'chain_letter_data.txt';
data = load ( filename );
fprintf ( 1, '\n' );
fprintf ( 1, ' Chain letter distance matrix read from "%s"\n', filename );
%
% pdist() requires the Statistics and Machine Learning Toolbox.
%
fprintf ( 1, '\n' );
fprintf ( 1, ' Test CANCELLED.\n' );
fprintf ( 1, ' Requires the Statistics and Machine Learning Toolbox\n' );
fprintf ( 1, ' Abnormal end of execution.\n' );
return
%
% Matlab's Statistical Toolbox can create a distance vector from a distance matrix,
% then apply single linkage clustering to that to create a tree structure, and then
% create a plot of the tree structure.
%
dv = pdist ( data );
dl = linkage ( dv, 'single' );
H = dendrogram ( dl, ...
'Labels', {'A','B','C','D','E','F','G','H','I','J','K'} );
%
% Request that lines be drawn thicker than the default value of 1.
%
set ( H, 'linewidth', 2 );
title ( 'Dendrogram for 11 chain letters A=1 through K=11', 'Fontsize', 16 );
filename = 'chain_letter_dendrogram.png';
print ( '-dpng', filename );
fprintf ( 1, '\n' );
fprintf ( 1, ' Graphics saved as "%s"\n', filename );
%
% Terminate.
%
fprintf ( 1, '\n' );
fprintf ( 1, 'chain_letter_dendrogram():\n' );
fprintf ( 1, ' Normal end of execution.\n' );
return
end