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% CSC 411: Machine Learning and Data Mining
%     Tutorial 2 (January 26th):Example for Decision tree algorithm
% Data example is referred from http://decisiontrees.net/?q=node/16
%
%Another short good Matlab tutorial:
%    http://cs.gmu.edu/~kosecka/cs803/MatlabTutorialCode.html
%For complete Matlab references:
%    http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html
%
% Rui Yan < ruiyan AT cs DOT toronto DOT edu >,January 26th 2007.
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clear;

%Entropy for the response
E_S = -9/14*log2(9/14)-5/14*log2(5/14)

%%%%%%%%%%%%%%Entropy and Gain Value for 'District' Attribute%%%%%%%%%
Gain=[0 0 0 0]; %Gain vector for holding the gain values for the four attributes
Entropy=zeros(4,3); %Entropy matrix for holding all the entropy values. 4X3 matrix

%Entropy for the District = Surburban
Entropy(1,1)=-0.6*log2(0.6)-0.4*log2(0.4)

%Entropy for the District = Rural
Entropy(1,2)=-log2(1)

%Entropy for the District = Urban
Entropy(1,3)=-0.6*log2(0.6)-0.4*log2(0.4)

%Gain value for 'District' attribute
Gain(1) = E_S-(5/14 * Entropy(1,1) +5/14 * Entropy(1,2) +4/14 *Entropy(1,3))

%%%%%%%%%%%%%%Entropy and Gain Value for 'House Type' Attribute%%%%%%%%%

%Entropy for the House Type = Detached
Entropy(2,1)=-0.5*log2(0.5)-0.5*log2(0.5)

%Entropy for the House Type = Semi-detached
Entropy(2,2)=-0.8*log2(0.8)-0.2*log2(0.2)

%Entropy for the Houes Type = Terrace
Entropy(2,3)=-0.6*log2(0.6)-0.4*log2(0.4)

%Gain value for 'House Type' attribute
Gain(2) = E_S-(4/14 * Entropy(2,1) +5/14 * Entropy(2,2) +5/14 *Entropy(2,3))
%%%%%%%%%%%%%%Entropy and Gain Value for 'Income' Attribute%%%%%%%%%

%Entropy for the Income = High
Entropy(3,1)=-4/7*log2(4/7)-3/7*log2(3/7)

%Entropy for the Income = Low
Entropy(3,2)=-1/7*log2(1/7)-6/7*log2(6/7)

%Gain value for 'Income' attribute
Gain(3)= E_S-(7/14 * Entropy(3,1) +7/14 * Entropy(3,2))

%%%%%%%%%%%%%%Entropy and Gain Value for 'Previous Customers' Attribute%%%%%%


%Entropy for the Previous Customers = No
Entropy(4,1)=-2/8*log2(2/8)-6/8*log2(6/8)

%Entropy for the Previous Customers = Responded
Entropy(4,2)=-3/6*log2(3/6)-3/6*log2(3/6)

%Gain value for 'Previous Customers' attribute
Gain(4) = E_S-(8/14 * Entropy(4,1) +6/14 * Entropy(4,2))

%sort Gain in ascending order
[ordered_Gain, index_Gain]=sort(Gain);
if index_Gain(4)==1
    disp('The ''District'' attribute has the largest Gain value');
elseif index_Gain(4)==2
    disp('The ''House Type'' attribute has the largest Gain value');
elseif index_Gain(4)==3
    disp('The ''Income'' attribute has the largest Gain value');
else
    disp('The ''Previous Customers'' attribute has the largest Gain value');
end

%draw a figure
figure;
bar(Gain');
xlabel('Four Attributes: District, House Type,Income, and Previous Customers');
ylabel('Gain value');
legend('District', 'House Type', 'Income', 'Previous Customers');
title('Gain value comparisons');

%save the matlab workspace
save decision_tree.mat