Data modeling based on MATLAB fuzzy binary decision tree

A list,

Fuzzy pattern tree (FPT) is a machine learning classification method, similar to binary descision diagram (BDD). Its internal nodes are labeled with generalized (fuzzy) logic and arithmetic operators, and leaf nodes are associated with (unary) fuzzy predicates on a given set of input attributes

Fuzzy Pattern Tree (FPT)

It is competitive with other competing machine learning approaches in terms of predictive performance, and due to the limited processing resources of iot nodes, it tends to generate compact models that are very attractive in terms of interpretation.

Its disadvantages are also obvious: its computational complexity is high and its runtime can become unacceptable.



Binary decision tree (BDD)

BDD is a data structure used to express Boolean functions. Is a directed acyclic graph based on Shannon decomposition.

If f is a Boolean function of a set of Boolean variables, and x is a variable in set X, shannon decomposition and its if-then-else(ite) form are



Where x and x-bar respectively represent event occurrence and event non-occurrence. Fx =1 (i.e. F1) and FX =0 (i.e. F2)

Represents Boolean functions for event occurrence and event non-occurrence respectively

The binary tree is expressed as follows:

Boolean function

Second, operation results

%%----- Main Program that should be run inorder to execute the code -----%%
 
% load the data file
load('earfeature15window700image.mat');
 
 
% Change following variable in case of number of user changes
noOfUsers = 100;
 
% Change following two variable in case you need to change ration of test
% and train case or when the number of data value for same user changes(right now its 7)
trainCasePerUser = 4;
testCasePerUser = 3;
 
if(testCasePerUser < 2)
    disp('testCasePerUser should be greater then 1')
    
else  
totalCasePerUser = trainCasePerUser + testCasePerUser;
% 3D matrix where 1st dimention is related the user, 2nd dimention related
% to datavalues per user and 3rd dimention are the feature values for datapoints 
test = zeros([noOfUsers testCasePerUser 35]);
train = zeros([noOfUsers trainCasePerUser 35]); % %this loop devides the data into testcases and trainingcase randomly
for i=1:noOfUsers
    
   % matrix p is the random permutation of interger 1 to total number of datavalues per user  
   p = randperm(totalCasePerUser,totalCasePerUser);
   
   % below two lines divide the data into tests and training data
   test(i,:,:) = T_S1(:,(i- 1)*totalCasePerUser + p(1:testCasePerUser))'; train(i,:,:) = T_S1(:,(i-1)*totalCasePerUser + p(testCasePerUser+1:totalCasePerUser))';
end
%% Following piece of code find creates the matching score matrix with 2 columns 
% 1st column has the value of matching score and 2nd column has value 1 if 
% its genuine and 0 if imposter
trainScore = zeros([noOfUsers*noOfUsers 2]);
testScore = zeros([noOfUsers*noOfUsers*(testCasePerUser- 1) 2]);
% loop that creates the matrix of training sample.
for i=1:noOfUsers
    for j=1:noOfUsers
        score = zeros([trainCasePerUser 1]);
        for k = 1:trainCasePerUser
            score(k) = norm(squeeze((test(i,1,:) - train(j,k,:))),2);
        end
        
        % take the min of distance to get the matching score
        trainScore((i- 1)*noOfUsers + j,1) = min(score);
        
        %  if the users are same then its genuine class else imposter
        if(i==j)
            trainScore((i- 1)*noOfUsers + j,2) = 1;
        else
            trainScore((i- 1)*noOfUsers + j,2) = 0;
        end        
    end
end
% loop that creates the matrix of testing sample
for z=0:testCasePerUser2 -
    for i=1:noOfUsers
        for j=1:noOfUsers
            score = zeros([trainCasePerUser 1]);
            for k = 1:trainCasePerUser
                score(k) = norm(squeeze((test(i,z+2,:) - train(j,k,:))),2);
            end
            testScore(z*noOfUsers*noOfUsers + (i- 1)*noOfUsers + j,1) = min(score);
            if(i==j)
                testScore(z*noOfUsers*noOfUsers + (i- 1)*noOfUsers + j,2) = 1;
            else
                testScore(z*noOfUsers*noOfUsers + (i- 1)*noOfUsers + j,2) = 0;
            end        
        end
    end
end
% find the geninue class datapoint and put them in Gtrain Matrix
Gtrain = trainScore(find(trainScore(:,2) = =1), :);
% find the imposter class datapoint and put them in Itrain Matrix
Itrain = trainScore(find(trainScore(:,2) = =0), :);
% Create the final training matrix with  score value in 1st column, membership 
% value in 2nd column and class in 3rd column for creating dicision tree%.change the membership function 2nd  column in case you want to use
% different membership funtion
Mtrain = [Gtrain(:,1) GaussianMembership(Gtrain(:,1)) Gtrain(:,2); Itrain(:,1) TrapezoidalMembership(Itrain(:,1)) Itrain(:,2)];
%Mtrain = [Gtrain(:,1) TrapezoidalMembership(Gtrain(:,1)) Gtrain(:,2); Itrain(:,1) TrapezoidalMembership(Itrain(:,1)) Itrain(:,2)]; %% This part of code deals with growing the decision tree % sort the training matrix according the matching score value.  [a b] = sort(Mtrain(:,1));
clear a;
data = Mtrain(b,:);
% grow the tree using sorted training matrix
tree = growTree( data );
%% This part of code deals with the predicting the class of testing score and
% calculation of FRR and FAR
testingSize = noOfUsers*noOfUsers*(testCasePerUser- 1);
geniuneTestingSize = noOfUsers*(testCasePerUser- 1);
trainingSize = noOfUsers*noOfUsers;
geniuneTrainingSize = noOfUsers;
pre = zeros([testingSize 2]);
% loop that predicts the values of all testing data
for i=1:testingSize
    pre(i,1) = predict(tree, testScore(i,:));
    pre(i,2) = testScore(i,2);
end
% calculation of FAR and FRR
FA = pre(find(pre(:,1) = =1 & pre(:,2) = =0), :); % False Acceptance FR = pre(find(pre(:,1) = =0 & pre(:,2) = =1), :); % False Rejection FAR = size(FA,1)/(testingSize-geniuneTestingSize); % False Acceptance Rate
FRR = size(FR,1)/geniuneTestingSize; % False Rejection Rate
%% histgram of normalized frequencies of matching score of Geniune and Imposter matching score
figure;
[m,yout] = hist(Itrain(:,1), 20);
m = m/(size(Itrain,1));
[n,xout] = hist(Gtrain(:,1), 20);
n = n/size(Gtrain,1);
bar(yout,m);
hold on;
bar(xout,n, 'r');
legend('Imposter Scores'.'Geniune Scores');
hold off;
end
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Third, note