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    %% Normalized Perceptron Rule
% A 2-input hard limit neuron is trained to classify 5 input vectors into two
% categories.  Despite the fact that one input vector is much bigger than the
% others, training with LEARNPN is quick.
%
% Copyright 1992-2014 The MathWorks, Inc.

%%
% Each of the five column vectors in X defines a 2-element input vectors, and a
% row vector T defines the vector's target categories.  Plot these vectors with
% PLOTPV.

X = [ -0.5 -0.5 +0.3 -0.1 -40; ...
      -0.5 +0.5 -0.5 +1.0 50];
T = [1 1 0 0 1];
plotpv(X,T);


%%
% Note that 4 input vectors have much smaller magnitudes than the fifth vector
% in the upper left of the plot.  The perceptron must properly classify the 5
% input vectors in X into the two categories defined by T.  
% 
% PERCEPTRON creates a new network with LEARPN learning rule, which is less
% sensative to large variations in input vector size than LEARNP (the
% default).
%
% The network is then configured with the input and target data which
% results in initial values for its weights and bias. (Configuration is
% normally not necessary, as it is done automatically by ADAPT and TRAIN.)

net = perceptron('hardlim','learnpn');
net = configure(net,X,T);

%%
% Add the neuron's initial attempt at classification to the plot.
%
% The initial weights are set to zero, so any input gives the same output and
% the classification line does not even appear on the plot.   Fear not... we are
% going to train it!

hold on
linehandle = plotpc(net.IW{1},net.b{1});

%%
% 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,
% plots the classification line, and continues until the error is zero.

E = 1;
while (sse(E))
   [net,Y,E] = adapt(net,X,T);
   linehandle = plotpc(net.IW{1},net.b{1},linehandle);
   drawnow;
end

%%
% Note that training with LEARNP took only 3 epochs, while solving the same
% problem with LEARNPN required 32 epochs.  Thus, LEARNPN does much better job
% than LEARNP when there are large variations in input vector size.

%%
% Now SIM can be used to classify any other input vector. For example, classify
% an input vector of [0.7; 1.2].
%
% A plot of this new point with the original training set shows how the network
% performs.  To distinguish it from the training set, color it red.

x = [0.7; 1.2];
y = net(x);
plotpv(x,y);
circle = findobj(gca,'type','line');
circle.Color = 'red';

%%
% Turn on "hold" so the previous plot is not erased.  Add the training set
% and the classification line to the plot.

hold on;
plotpv(X,T);
plotpc(net.IW{1},net.b{1});
hold off;

%%
% Finally, zoom into the area of interest.
%
% The perceptron correctly classified our new point (in red) as category "zero"
% (represented by a circle) and not a "one" (represented by a plus). The
% perceptron learns properly in much shorter time in spite of the outlier
% (compare with the "Outlier Input Vectors" example).

axis([-2 2 -2 2]);