Matlab code for Newtons optimization for Logistic Regression

% % this is for two class problem for more than two class code changes
% % ————-Parameters————-
% numIteration =1000; The Number of maximum iterations
% % errorBound = 0.0001; This is the permissible error.
% The experiments have been done keep in view both the error condition
% reached or maximum iteration reached whichever comes first.
% % eta = 0.5; This is the learning rate, experiments have been
% done on various learning rates
% % ————-Parameters————-
% %

function logit_Newton_1()
disp(‘..Starting logistic regression Algorithm….’);

%reading data

A = load('BananaData.mat');
data = A.data;    
[N,col]= size(data);

vtot=[0, 0, 0, 0,0, 0,  0 , 0];

%5 folds with 70-30 ratio
for i = 1:5

    P=.3;
    groups=data(:,3);
    [train,test] = crossvalind('holdout',groups, P);
    train1= data(train, 1: 3);
    test1=data(test, 1:3);
    [trainLengthRow, trainLengthCol]=size(train1);
    [rowtest,coltest]= size(test1);

    trainingSet = train1(1:trainLengthRow, 1 : trainLengthCol -1 );
    trainingLabels = train1(1:trainLengthRow, trainLengthCol );

    %converting data to 1 and 0 class instead of 1 and -1 class as
    %using logit
    for p=1:trainLengthRow
        if trainingLabels(p)== -1
            trainingLabels(p) = 0;
        end
    end


    testSet = test1(1:rowtest, 1 : coltest -1 );
    testLabels = test1(1:rowtest, coltest );

    %converting data to 1 and 0 class instead of 1 and -1 class as
    %using logit        
    for p=1:rowtest
        if testLabels(p)== -1
            testLabels(p) = 0;
        end
    end

[weights] = trainLogReg( trainingSet,trainingLabels);

[correctlyClassified,count0,count1,unClassified,v] = testNewton(testSet,testLabels, weights) ;
vtot = vtot +v ;
end

% taking average of all such entries
disp(‘TP, TN, FP, FN, TP/(TP+FP), TP/P, 2PR / (P+R) , correctlyClassified/trainLengthRow’);
vtot = vtot ./ 5

end

function [weights] = trainLogReg( trainingSet,trainingLabels)

numIteration =1000;
eta = 0.5;            
errorBound = 0.0001;

[trainLengthRow, trainLengthCol] = size(trainingSet); 
errorVec=ones(trainLengthCol+1);

weightsFinal = zeros(trainLengthCol+1);

W_Old(1:trainLengthCol+1) = 0;
W_New(1:trainLengthCol+1) = 0;

P(1:trainLengthRow) = 0;
Y =  trainingLabels';
X(1:trainLengthRow , 1:trainLengthCol+1) = 0;
X(1:trainLengthRow ,1) = 1;
X(1:trainLengthRow ,2:trainLengthCol+1) = trainingSet(1:trainLengthRow,1:trainLengthCol);

error=1.0;
k=1;

while ((error >= errorBound ) && (k < numIteration))
error=0;
    for t=1: trainLengthRow
        sum = W_Old(1);

        for j=1: trainLengthCol
        sum = sum + W_Old(j+1)*trainingSet(t,j);
        end;

        P(t) = 1/(1+ exp(-1*sum));

    end;


Z= (X') * (Y-P)';
W = diag(P.* (1-P));
Hessian =  X' * W * X;
etaMatrix(1:3) = eta;
W_New = W_Old + etaMatrix .* (Hessian \ Z)'  ;

% errorVec = 0.5* (Y’-XW_New’).(Y’-X*W_New’);
%
% for i = 1: trainLengthCol+1
% error=error+errorVec(i);
% end

error= 0;
W_New  
k
error


k=k+1;
W_Old = W_New;

y1(1:trainLengthRow)=0;    

for i =1: trainLengthRow

    sum = W_Old(1);

    for j=1: trainLengthCol
    sum = sum +  W_Old(j+1)*trainingSet(i,j);
    end;

    y1(i) = 1/(1+ exp(-1*sum));                
    error = 0.5 * (y1(i) -Y(i) ) * (y1(i) - Y(i) );
 end;

error
end

weights = W_Old;

%Now computing the final y using the final weights
 disp('final weights :  number of iterations : error');
 W_Old
 k
 error



%The following is for figure generation
%Now computing the final y using the final weights
 disp('final weights :  number of iterations : error');
 W_Old
 k
 error

y1(1:trainLengthRow)=0;
y0(1:trainLengthRow)=0;

for i =1: trainLengthRow

    sum = W_Old(1);

    for j=1: trainLengthCol
    sum = sum +  W_Old(j+1)*trainingSet(i,j);
    end;

    y1(i) = 1/(1+ exp(-1*sum));
    y0(i) = 1/(1+ exp(sum));

 end;

 data(1:trainLengthRow, 1:trainLengthCol+1)=0;
 data(1:trainLengthRow, 1:trainLengthCol)= trainingSet;
 for p=1:trainLengthRow
   data(p, trainLengthCol+1)= y1(p);
 end;

 %figure
% parallelcoords(data,'Labels',labels);

 for p=1:trainLengthRow
   x1(p)= trainingSet(p,1);
 end;

 for p=1:trainLengthRow
   x2(p)= trainingSet(p,2);
 end;


 for p=1:trainLengthRow
   yOrginal(p)= trainingLabels(p);
 end;

%
% figure(1)
% hold on;
% scatter3(x1,x2,trainingLabels,10,’g’);
% axis([-5,5,-5,5,-5,5])

 %figure(1)     
 %plot3(x1,x2,y1); 
 %axis([-5,5,-5,5,-5,5])

 figure(1)     
 hold on;     
 uniqueClasses=unique(trainingLabels)
 positive = uniqueClasses(1);
 index=find(trainingLabels==positive);
  plot3(x1(index),x2(index),trainingLabels(index), ['r','o'],'MarkerFaceColor','r')
 negative = uniqueClasses(2);
 index2=find(trainingLabels==negative);
 plot3(x1(index2),x2(index2),trainingLabels(index2), ['g','o'],'MarkerFaceColor','g')


 xx=(-10:1:10);
 yy=(-10:1:10);
 [xx1,yy1]=meshgrid(xx,yy);

 sum1 = -1 .* (W_Old(1)+W_Old(2).*xx1+W_Old(3).*yy1);

 zz= 1 ./(1 + expm(sum1));     
 [p1,m1]=size(zz);

 for p=1: p1
     for m=1:m1
              expVal = exp(sum1(p,m));
             zz(p,m) = 1 / (1+ expVal);
            end
     end
 end


 figure(2)
 surf(xx1,yy1,zz);
 title('title');
 xlabel('x');
 ylabel('y')
 zlabel('z');

end

function [correctlyClassified,count0,count1,unClassified,v] = testNewton(testSet,testLabels, weights)

correctlyClassified = 0;
count0 = 0; count1=0;   TP=0;    TN=0;     FP=0;     FN =0; P=0; R=0; F=0;

[testLengthRow,testLengthCol]=size(testSet);
unClassified(1:10 ,1: testLengthCol) = 0;

% checking accuracy by  number of correctly classified   

for k=(1: testLengthRow )
    x=[1, testSet(k,1:testLengthCol)];
    O1=    x' .* weights' ;

    %computing the value of vector with plane
    sum =0;
    for p=1:length(O1)
        sum = sum +O1(p);
    end

     y1x = 1/(1+ exp(-1*sum));
     if(y1x>=0.5)
         %disp('class 1');
         O =1;
     else
         %disp('class 0');
         O =0;
     end

     %    error as output approaching target
    if (O == testLabels(k))
        % correctly classified examples
        correctlyClassified=correctlyClassified+1;

        %compute  TP, TN
        if(testLabels(k)==1)
            TP = TP+1;
        else
            TN = TN +1;
        end

    else
        % wrongly classified examples
        if(testLabels(k)==1)
            FN = FN+1;
        else
            FP = FP +1;
        end
        %storing 5 misclassified  classes from each class
        if(count1<5 && testLabels(k)==1)
            count1 = count1 + 1;
            unClassified(count1,1: testLengthCol) = testSet(k,1: testLengthCol);
        end
        if(count0<5 && testLabels(k)==0 )
            count0 = count0 + 1;
            unClassified(count0,1: testLengthCol) = testSet(k,1: testLengthCol);                
        end
    end

end

  k
P= TP/(TP+FP)
R=  TP/(TP+FN)
v=[TP,    TN,     FP,     FN,     P,     R,      2*P*R / (P+R) , correctlyClassified/testLengthRow]
disp('TP,    TN,     FP,     FN,     TP/(TP+FP),      TP/P,      2*P*R / (P+R) , correctlyClassified/trainLengthRow');


 unClassified;
 accuracy = correctlyClassified/testLengthRow  ;   
 accuracy

end