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Matlab code for Radial Basis Functions

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%Matlab code for Radial Basis Functions clc;

x=-1:0.05:1;

%generating training data with Random Noise for 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 data t=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); end end W=inv(train)*y';

% Testing the trained RBF xtest=-1:0.01:1;

%ytest is the desired output

ytest=1.2*sin(pi*xtest)-cos(2.4*pi*xtest);

% Framing the interpolation matrix for test data t1=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); end end actual_test=test*W;

% Plotting the Performance of the network figure;

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 Random clc;

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% 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 samples idx=randperm(numel(x));

l=x(idx(1:20)); t=sort(l); centre=t';

% Framing the interpolation matrix for training data t=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); end end I=eye(20);

lamda=0; % Regularization factor

W=inv((gtrain'*gtrain)+ lamda * I)*gtrain'*y'; % Testing the trained RBF

xtest=-1:0.01:1

%ytest is the desired output for 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 data t2=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); end end dtest=gtest*W;

% Plotting the performance of the network figure;

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 Functions clc;

x=-1:0.05:1;

(3)

for 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 data t=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); end end

% Determining the weight matrix I= 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 RBF xtest=-1:0.01:1;

%ytest is the desired output

ytest=1.2*sin(pi*xtest)-cos(2.4*pi*xtest);

% Framing the interpolation matrix for test data t1=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); end end for h=1:10 actual_test(:,h)=test*W(:,h); end

% Plotting the Performance of the network figure; for h=1:5 subplot(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'); end figure; m=0; for h=1:5 m=5+h; subplot(3,2,h); plot(xtest,ytest,'b-',xtest,actual_test(:,m),'r+'); xlabel('Xtest value'); ylabel('Ytest value');

(4)

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 Random clc;

% 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

(5)

% Generating 20 Fixed Random Centres from the samples idx=randperm(numel(x));

l=x(idx(1:20)); t=sort(l); centre=t';

% Framing the interpolation matrix for training data t=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); end end I=eye(20); for h=1:10

lamda=h; % Regularization factor

W(:,h)=inv((gtrain'*gtrain)+ lamda * I)*gtrain'*y'; end

% Testing the trained RBF xtest=-1:0.01:1

%ytest is the desired output for 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 data t2=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); end end for h=1:10 dtest(:,h)=gtest*W(:,h); end figure; for h=1:5 subplot(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'); end figure; m=0; for h=1:5 m=5+h; subplot(3,2,h); plot(xtest,ytest,'b-',xtest,dtest(:,m),'r+'); xlabel('Xtest value');

(6)

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 images clc; load Features_color_histogram; % image_features_train % scene_labels_train % image_features_test % scene_labels_test

% Framing the input matrix x=zeros(60,5);

for i=1:length(x) for j=1:4

(7)

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 variables InputSize=5;

NoofSamples=60; OutputSizeX=10; OutputSizeY=10; N=1000;

% Initializing the parameters of the Kohonen Network InitialLearningRate=0.1; T2=N; InitialEffectiveWidth=5; T1=N/(log(InitialEffectiveWidth)); EffectiveWidth=InitialEffectiveWidth; LearningRate=InitialLearningRate; j=1;

% Getting the Coodinates for the output map for row=1:OutputSizeX for column=1:OutputSizeY MapX(j)=row; MapY(j)=column; j=j+1; end end

% Assigning initial weights for synapses NumberOfNodes=OutputSizeX*OutputSizeY; w=rand(InputSize,NumberOfNodes);

% Iterating through 1000 iterations for 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

(8)

for 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 network figure; 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 images clc; load Features_color_histogram; % image_features_train % scene_labels_train % image_features_test % scene_labels_test

% Framing the input matrix k=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;

(9)

x(i,j)=k; k=k+1; end

x=x';

% Assigning the input values of the network variables InputSize=5;

NoofSamples=60; OutputSizeX=10; OutputSizeY=10; N=1000;

% Initializing the parameters of the Kohonen Network InitialLearningRate=0.1; T2=N; InitialEffectiveWidth=5; T1=N/(log(InitialEffectiveWidth)); EffectiveWidth=InitialEffectiveWidth; LearningRate=InitialLearningRate; j=1;

% Getting the Coodinates for the output map for row=1:OutputSizeX for column=1:OutputSizeY MapX(j)=row; MapY(j)=column; j=j+1; end end

% Assigning initial weights for synapses NumberOfNodes=OutputSizeX*OutputSizeY; w=rand(InputSize,NumberOfNodes);

% Iterating through 1000 iterations for 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 Map for i=1:NoofSamples

(10)

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 Map for 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; end end

%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 images DisplayImageMatrix(indices_display);

% Self Organizing Map cluster and classify scene images clc; load Features_color_histogram; % image_features_train % scene_labels_train % image_features_test % scene_labels_test

% Framing the input matrix 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)=scene_labels_train(:,i); end x=x';

(11)

InputSize=5; NoofSamples=60; OutputSizeX=10; OutputSizeY=10; N=1000;

% Initializing the parameters of the Kohonen Network InitialLearningRate=0.1; T2=N; InitialEffectiveWidth=5; T1=N/(log(InitialEffectiveWidth)); EffectiveWidth=InitialEffectiveWidth; LearningRate=InitialLearningRate; j=1;

% Getting the Coodinates for the output map for row=1:OutputSizeX for column=1:OutputSizeY MapX(j)=row; MapY(j)=column; j=j+1; end end

% Assigning initial weights for synapses NumberOfNodes=OutputSizeX*OutputSizeY; w=rand(InputSize,NumberOfNodes);

% Iterating through 1000 iterations for 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

(12)

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 Map for 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 network figure; 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; end subplot(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

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