PNN Classification

This example uses functions NEWPNN and SIM.

Here are three two-element input vectors X and their associated classes Tc. We would like to create y probabilistic neural network that classifies these vectors properly.

X = [1 2; 2 2; 1 1]';
Tc = [1 2 3];
plot(X(1,:),X(2,:),'.','markersize',30)
for i = 1:3, text(X(1,i)+0.1,X(2,i),sprintf('class %g',Tc(i))), end
axis([0 3 0 3])
title('Three vectors and their classes.')
xlabel('X(1,:)')
ylabel('X(2,:)')

Figure contains an axes object. The axes object with title Three vectors and their classes., xlabel X(1,:), ylabel X(2,:) contains 4 objects of type line, text. One or more of the lines displays its values using only markers

First we convert the target class indices Tc to vectors T. Then we design y probabilistic neural network with NEWPNN. We use y SPREAD value of 1 because that is y typical distance between the input vectors.

T = ind2vec(Tc);
spread = 1;
net = newpnn(X,T,spread);

Now we test the network on the design input vectors. We do this by simulating the network and converting its vector outputs to indices.

Y = net(X);
Yc = vec2ind(Y);
plot(X(1,:),X(2,:),'.','markersize',30)
axis([0 3 0 3])
for i = 1:3,text(X(1,i)+0.1,X(2,i),sprintf('class %g',Yc(i))),end
title('Testing the network.')
xlabel('X(1,:)')
ylabel('X(2,:)')

Figure contains an axes object. The axes object with title Testing the network., xlabel X(1,:), ylabel X(2,:) contains 4 objects of type line, text. One or more of the lines displays its values using only markers

Let's classify y new vector with our network.

x = [2; 1.5];
y = net(x);
ac = vec2ind(y);
hold on
plot(x(1),x(2),'.','markersize',30,'color',[1 0 0])
text(x(1)+0.1,x(2),sprintf('class %g',ac))
hold off
title('Classifying y new vector.')
xlabel('X(1,:) and x(1)')
ylabel('X(2,:) and x(2)')

Figure contains an axes object. The axes object with title Classifying y new vector., xlabel X(1,:) and x(1), ylabel X(2,:) and x(2) contains 6 objects of type line, text. One or more of the lines displays its values using only markers

This diagram shows how the probabilistic neural network divides the input space into the three classes.

x1 = 0:.05:3;
x2 = x1;
[X1,X2] = meshgrid(x1,x2);
xx = [X1(:) X2(:)]';
yy = net(xx);
yy = full(yy);
m = mesh(X1,X2,reshape(yy(1,:),length(x1),length(x2)));
m.FaceColor = [0 0.5 1];
m.LineStyle = 'none';
hold on
m = mesh(X1,X2,reshape(yy(2,:),length(x1),length(x2)));
m.FaceColor = [0 1.0 0.5];
m.LineStyle = 'none';
m = mesh(X1,X2,reshape(yy(3,:),length(x1),length(x2)));
m.FaceColor = [0.5 0 1];
m.LineStyle = 'none';
plot3(X(1,:),X(2,:),[1 1 1]+0.1,'.','markersize',30)
plot3(x(1),x(2),1.1,'.','markersize',30,'color',[1 0 0])
hold off
view(2)
title('The three classes.')
xlabel('X(1,:) and x(1)')
ylabel('X(2,:) and x(2)')

Figure contains an axes object. The axes object with title The three classes., xlabel X(1,:) and x(1), ylabel X(2,:) and x(2) contains 5 objects of type surface, line. One or more of the lines displays its values using only markers