%Matlab code for Radial Basis Functionsclc;x=-1:0.05:1;%generating training data with Random Noisefor i=1:length(x)y(i)=1.2*sin(pi*x(i))-cos(2.4*pi*x(i))+0.3*randn;end% Framing the interpolation matrix for training datat=length(x);for i=1:1:t for j=1:1:t h=x(i)-x(j); k=h^2/.02; train(i,j)=exp(-k); endendW=inv(train)*y';% Testing the trained RBFxtest=-1:0.01:1;%ytest is the desired outputytest=1.2*sin(pi*xtest)-cos(2.4*pi*xtest);% Framing the interpolation matrix for test datat1=length(xtest);t=length(x);for i=1:1:t1 for j=1:1:t h=xtest(i)-x(j); k=h^2/.02; test(i,j)=exp(-k); endendactual_test=test*W;% Plotting the Performance of the networkfigure;plot(xtest,ytest,'b-',xtest,actual_test,'r+');xlabel('Xtest value');ylabel('Ytest value');h = legend('Desired output','Approximated curve',2);set(h);

%Matlab code for Fixed Centres Selected at Randomclc;% Training sampling 41 points in the range of [-1,1]x=-1:0.05:1;%generating training data for i=1:length(x)y(i)=1.2*sin(pi*x(i))-cos(2.4*pi*x(i))+0.3*randn;end% Generating 20 Fixed Random Centres from the samplesidx=randperm(numel(x));l=x(idx(1:20));t=sort(l);centre=t';% Framing the interpolation matrix for training datat=length(x);t1=length(centre);for i=1:1:t for j=1:1:t1 h=x(i)-centre(j); k=h^2/0.02; gtrain(i,j)=exp(-k); endend I=eye(20); lamda=0; % Regularization factor W=inv((gtrain'*gtrain)+ lamda * I)*gtrain'*y';% Testing the trained RBFxtest=-1:0.01:1%ytest is the desired outputfor i=1:length(xtest)ytest(i)=1.2*sin(pi*xtest(i))-cos(2.4*pi*xtest(i));end% Framing the interpolation matrix for test datat2=length(xtest);for i=1:1:t2 for j=1:1:t1 h=xtest(i)-centre(j); k=h^2/.02; gtest(i,j)=exp(-k); endenddtest=gtest*W;% Plotting the performance of the networkfigure;plot(xtest,ytest,'b-',xtest,dtest,'r+');xlabel('Xtest value');ylabel('Ytest value');h = legend('Desired output','Approximated curve',2);set(h);

%Matlab code for Radial Basis Functionsclc;x=-1:0.05:1;%generating training data with Random Noisefor i=1:length(x)y(i)=1.2*sin(pi*x(i))-cos(2.4*pi*x(i))+0.3*randn;end% Framing the interpolation matrix for training datat=length(x);for i=1:1:t for j=1:1:t h=x(i)-x(j); k=h^2/.02; train(i,j)=exp(-k); endend% Determining the weight matrixI= eye(41);q=0;for h=1:10 lamda=h; % Regularization factor W(:,h)=inv((train'*train)+ lamda * I)*train'*y';end% Testing the trained RBFxtest=-1:0.01:1;%ytest is the desired outputytest=1.2*sin(pi*xtest)-cos(2.4*pi*xtest);% Framing the interpolation matrix for test datat1=length(xtest);t=length(x);for i=1:1:t1 for j=1:1:t h=xtest(i)-x(j); k=h^2/.02; test(i,j)=exp(-k); endendfor h=1:10actual_test(:,h)=test*W(:,h);end% Plotting the Performance of the networkfigure;for h=1:5subplot(3,2,h);plot(xtest,ytest,'b-',xtest,actual_test(:,h),'r+');xlabel('Xtest value');ylabel('Ytest value');text(-0.9,1.5,['Regularization factor = ',num2str(h)]);g = legend('Desired Output','Approximated curve',2);set(g,'box','off');endfigure;m=0;

for h=1:5m=5+h;subplot(3,2,h);plot(xtest,ytest,'b-',xtest,actual_test(:,m),'r+');xlabel('Xtest value');ylabel('Ytest value');text(-0.9,1.5,['Regularization factor =',num2str(m)]);g = legend('Desired Output','Approximated curve',2);set(g,'box','off');end

%Matlab code for Fixed Centres Selected at Randomclc;% Training sampling 41 points in the range of [-1,1]x=-1:0.05:1;%generating training data for i=1:length(x)y(i)=1.2*sin(pi*x(i))-cos(2.4*pi*x(i))+0.3*randn;end% Generating 20 Fixed Random Centres from the samplesidx=randperm(numel(x));l=x(idx(1:20));t=sort(l);centre=t';% Framing the interpolation matrix for training datat=length(x);t1=length(centre);for i=1:1:t for j=1:1:t1 h=x(i)-centre(j); k=h^2/0.02; gtrain(i,j)=exp(-k); endend I=eye(20); for h=1:10 lamda=h; % Regularization factor W(:,h)=inv((gtrain'*gtrain)+ lamda * I)*gtrain'*y'; end% Testing the trained RBFxtest=-1:0.01:1%ytest is the desired outputfor i=1:length(xtest)ytest(i)=1.2*sin(pi*xtest(i))-cos(2.4*pi*xtest(i));end% Framing the interpolation matrix for test datat2=length(xtest);for i=1:1:t2 for j=1:1:t1 h=xtest(i)-centre(j); k=h^2/.02; gtest(i,j)=exp(-k); endendfor h=1:10dtest(:,h)=gtest*W(:,h);endfigure;for h=1:5subplot(3,2,h);plot(xtest,ytest,'b-',xtest,dtest(:,h),'r+');xlabel('Xtest value');ylabel('Ytest value');text(-0.9,1.5,['Regularization factor = ',num2str(h)]);

g = legend('Desired Output','Approximated curve',2);set(g,'box','off');endfigure;m=0;for h=1:5m=5+h;subplot(3,2,h);plot(xtest,ytest,'b-',xtest,dtest(:,m),'r+');xlabel('Xtest value');ylabel('Ytest value');text(-0.9,1.5,['Regularization factor =',num2str(m)]);g = legend('Desired Output','Approximated curve',2);set(g,'box','off');end

% Self Organizing Map cluster and classify scene imagesclc;load Features_color_histogram;% image_features_train % scene_labels_train % image_features_test % scene_labels_test % Framing the input matrixx=zeros(60,5);for i=1:length(x) for j=1:4 x(i,j)=image_features_train(i,j); end j=j+1; x(i,j)=scene_labels_train(:,i); end x=x';% Assigning the input values of the network variablesInputSize=5;NoofSamples=60;OutputSizeX=10;OutputSizeY=10;N=1000;% Initializing the parameters of the Kohonen NetworkInitialLearningRate=0.1;T2=N;InitialEffectiveWidth=5;T1=N/(log(InitialEffectiveWidth)); EffectiveWidth=InitialEffectiveWidth;LearningRate=InitialLearningRate;j=1;% Getting the Coodinates for the output mapfor row=1:OutputSizeX for column=1:OutputSizeY MapX(j)=row; MapY(j)=column; j=j+1; endend% Assigning initial weights for synapsesNumberOfNodes=OutputSizeX*OutputSizeY;w=rand(InputSize,NumberOfNodes);% Iterating through 1000 iterationsfor epoch=1:N % Drawing a sample vector r=randint(1,1,[1 60]); x(:,r); %Randomly drawn vector %competition phase %Determining the winner neuron for j=1:NumberOfNodes Eucld(j)=norm(x(:,r)-w(:,j));

end [y,v]=min(Eucld); winner=v;%Winning Neuron % Co-operation and adaptaion phase for j=1:NumberOfNodes d=sqrt((MapX(j)-MapX(winner))^2+(MapY(j)-MapY(winner))^2); h=exp(-(d^2)/(2*(EffectiveWidth^2))); w(:,j)=w(:,j)+LearningRate*h*(x(:,r)-w(:,j)); end %Varying the learning Rate and Effective width for every epoch LearningRate=InitialLearningRate*exp(-epoch/T2); EffectiveWidth=InitialEffectiveWidth*exp(-epoch/T1);end% Framing the SOM Output Mapfor i=1:NoofSamples % Determining the winner neuron for j=1:NumberOfNodes Eucld(j)=norm(x(:,i)-w(:,j)); scene(j)=w(5,j); end [y1,v1]=min(Eucld); label1(i)=round(scene(v1)); winner1(i)=v1; end% Plotting the performance of the networkfigure;for i=1:NoofSamples plot(i,winner1(i),'*') text(i+0.5,winner1(i),num2str(label1(i))); xlabel('No of samples') ylabel('Output neurons') h = legend('Winner neuron',2); set(h,'box','off'); grid on; hold on;end

% Self Organizing Map cluster and classify scene imagesclc;load Features_color_histogram;% image_features_train % scene_labels_train % image_features_test % scene_labels_test % Framing the input matrixk=1; x=zeros(60,5);for i=1:length(x) for j=1:4 x(i,j)=image_features_train(i,j); end j=j+1; x(i,j)=k; k=k+1;end x=x';% Assigning the input values of the network variablesInputSize=5;NoofSamples=60;OutputSizeX=10;OutputSizeY=10;N=1000;% Initializing the parameters of the Kohonen NetworkInitialLearningRate=0.1;T2=N;InitialEffectiveWidth=5;T1=N/(log(InitialEffectiveWidth)); EffectiveWidth=InitialEffectiveWidth;LearningRate=InitialLearningRate;j=1;% Getting the Coodinates for the output mapfor row=1:OutputSizeX for column=1:OutputSizeY MapX(j)=row; MapY(j)=column; j=j+1; endend% Assigning initial weights for synapsesNumberOfNodes=OutputSizeX*OutputSizeY;w=rand(InputSize,NumberOfNodes);% Iterating through 1000 iterationsfor epoch=1:N % Drawing a sample vector r=randint(1,1,[1 60]); x(:,r); %Randomly drawn vector %competition phase %Determining the winner neuron

for j=1:NumberOfNodes Eucld(j)=norm(x(:,r)-w(:,j)); end [y,v]=min(Eucld); winner=v;%Winning Neuron % Co-operation and adaptaion phase for j=1:NumberOfNodes d=sqrt((MapX(j)-MapX(winner))^2+(MapY(j)-MapY(winner))^2); h=exp(-(d^2)/(2*(EffectiveWidth^2))); w(:,j)=w(:,j)+LearningRate*h*(x(:,r)-w(:,j)); end %Varying the learning Rate and Effective width for every epoch LearningRate=InitialLearningRate*exp(-epoch/T2); EffectiveWidth=InitialEffectiveWidth*exp(-epoch/T1);end% Framing the SOM Output Mapfor i=1:NoofSamples % Determining the winner neuron for j=1:NumberOfNodes Eucld(j)=norm(x(:,i)-w(:,j)); scene(j)=w(5,j); end [y1,v1]=min(Eucld); label1(i)=round(scene(v1)); winner1(i)=v1; winner2(i)=w(5,v1); % Framing the SOM Output Mapfor i=1:NumberOfNodes for j=1:NoofSamples Eucld(j)=norm(x(:,j)-w(:,i)); scene(j)=x(5,j); end [y1,v1]=min(Eucld); label1(i)=round(scene(v1)); winner1(i)=v1; endend %mapping 60 sample to output layer of SOM (10X10)j=1;for row=1:OutputSizeX for column=1:OutputSizeY indices_display(row,column)=winner1(j); j=j+1; end end % Plotting semantic map for the texture imagesDisplayImageMatrix(indices_display);

% Self Organizing Map cluster and classify scene imagesclc; load Features_color_histogram;% image_features_train % scene_labels_train % image_features_test % scene_labels_test % Framing the input matrixx=zeros(60,5);for i=1:length(x) for j=1:4 x(i,j)=image_features_train(i,j); end j=j+1; x(i,j)=scene_labels_train(:,i); end x=x';% Assigning the input values of the network variablesInputSize=5;NoofSamples=60;OutputSizeX=10;OutputSizeY=10;N=1000; % Initializing the parameters of the Kohonen NetworkInitialLearningRate=0.1;T2=N;InitialEffectiveWidth=5;T1=N/(log(InitialEffectiveWidth)); EffectiveWidth=InitialEffectiveWidth;LearningRate=InitialLearningRate;j=1; % Getting the Coodinates for the output mapfor row=1:OutputSizeX for column=1:OutputSizeY MapX(j)=row; MapY(j)=column; j=j+1; endend % Assigning initial weights for synapsesNumberOfNodes=OutputSizeX*OutputSizeY;w=rand(InputSize,NumberOfNodes); % Iterating through 1000 iterationsfor epoch=1:N % Drawing a sample vector r=randint(1,1,[1 60]);

x(:,r); %Randomly drawn vector %competition phase %Determining the winner neuron for j=1:NumberOfNodes Eucld(j)=norm(x(:,r)-w(:,j)); end [y,v]=min(Eucld); winner=v;%Winning Neuron % Co-operation and adaptaion phase for j=1:NumberOfNodes d=sqrt((MapX(j)-MapX(winner))^2+(MapY(j)-MapY(winner))^2); h=exp(-(d^2)/(2*(EffectiveWidth^2))); w(:,j)=w(:,j)+LearningRate*h*(x(:,r)-w(:,j)); end %Varying the learning Rate and Effective width for every epoch LearningRate=InitialLearningRate*exp(-epoch/T2); EffectiveWidth=InitialEffectiveWidth*exp(-epoch/T1);end y=zeros(30,5);for i=1:length(y) for j=1:4 y(i,j)=image_features_test(i,j); end j=j+1; y(i,j)=scene_labels_test(:,i); end y=y';NoofSamples=30;% Framing the SOM Output Mapfor i=1:NoofSamples % Determining the winner neuron for j=1:NumberOfNodes Eucld(j)=norm(y(:,i)-w(:,j)); scene(j)=w(5,j); end [y2,v2]=min(Eucld); label2(i)=round(scene(v2)); winner2(i)=v2; recognition_rate(i)= label2(i)-scene_labels_test(i); end % Plotting the performance of the networkfigure;subplot(2,1,1)for i=1:NoofSamples plot(i,winner2(i),'*')

text(i+0.5,winner2(i),num2str(label2(i))); xlabel('No of samples') ylabel('Output neurons') h = legend('Winner neuron',2); set(h,'box','on'); grid on; hold on;endsubplot(2,1,2)for i=1:NoofSamples plot(i,recognition_rate(i),'*') xlabel('No of samples') ylabel('Recognition error') h = legend('Recognition error',2); set(h,'box','on'); hold on;end