Classification of a 4-class problem with a perceptron

PROBLEM DESCRIPTION: Perceptron network with 2-inputs and 2-outputs is trained to classify input vectors into 4 categories

Define data
Prepare inputs & outputs for perceptron training
Create a perceptron
Train a perceptron
How to use trained perceptron

Define data

close all, clear all, clc, format compact

% number of samples of each class
K = 30;

% define classes
q = .6; % offset of classes
A = [rand(1,K)-q; rand(1,K)+q];
B = [rand(1,K)+q; rand(1,K)+q];
C = [rand(1,K)+q; rand(1,K)-q];
D = [rand(1,K)-q; rand(1,K)-q];
% plot classes
plot(A(1,:),A(2,:),'bs')
hold on
grid on
plot(B(1,:),B(2,:),'r+')
plot(C(1,:),C(2,:),'go')
plot(D(1,:),D(2,:),'m*')
% text labels for classes
text(.5-q,.5+2*q,'Class A')
text(.5+q,.5+2*q,'Class B')
text(.5+q,.5-2*q,'Class C')
text(.5-q,.5-2*q,'Class D')

% define output coding for classes
a = [0 1]';
b = [1 1]';
c = [1 0]';
d = [0 0]';
% % Why this coding doesn't work?
% a = [0 0]';
% b = [1 1]';
% d = [0 1]';
% c = [1 0]';
% % Why this coding doesn't work?
% a = [0 1]';
% b = [1 1]';
% d = [1 0]';
% c = [0 1]';

Prepare inputs & outputs for perceptron training

% define inputs (combine samples from all four classes)
P = [A B C D];
% define targets
T = [repmat(a,1,length(A)) repmat(b,1,length(B)) ...
     repmat(c,1,length(C)) repmat(d,1,length(D)) ];
%plotpv(P,T);

Create a perceptron

net = perceptron;

Train a perceptron

ADAPT returns a new network object that performs as a better classifier, the network output, and the error. This loop allows the network to adapt for xx passes, plots the classification line, and continues until the error is zero.

E = 1;
net.adaptParam.passes = 1;
linehandle = plotpc(net.IW{1},net.b{1});
n = 0;
while (sse(E) & n<1000)
   n = n+1;
   [net,Y,E] = adapt(net,P,T);
   linehandle = plotpc(net.IW{1},net.b{1},linehandle);
   drawnow;
end
% show perceptron structure
view(net);

How to use trained perceptron

% For example, classify an input vector of [0.7; 1.2]
p = [0.7; 1.2]
y = net(p)
% compare response with output coding (a,b,c,d)