Learning Vector Quantization

An LVQ network is trained to classify input vectors according to given targets.

Copyright 1992-2002 The MathWorks, Inc. $Revision: 1.14 $ $Date: 2002/03/29 19:36:12 $

Let P be 10 2-element example input vectors and C be the classes these vectors fall into. These classes can be transformed into vectors to be used as targets, T, with IND2VEC.

P = [-3 -2 -2  0  0  0  0 +2 +2 +3;
      0 +1 -1 +2 +1 -1 -2 +1 -1  0];
C = [1 1 1 2 2 2 2 1 1 1];
T = ind2vec(C);

Here the data points are plotted. Red = class 1, Cyan = class 2. The LVQ network represents clusters of vectors with hidden neurons, and groups the clusters with output neurons to form the desired classes.

colormap(hsv);
plotvec(P,C)
title('Input Vectors');
xlabel('P(1)');
ylabel('P(2)');

NEWLVQ creates an LVQ layer and here takes four arguments: Rx2 matrix of min and max values for R input elements, number of hidden neurons, element vector of typical class percentages, and learning rate,

net = newlvq(minmax(P),4,[.6 .4],0.1);

The competitive neuron weight vectors are plotted as follows.

hold on
W1 = net.IW{1};
plot(W1(1,1),W1(1,2),'ow')
title('Input/Weight Vectors');
xlabel('P(1), W(1)');
ylabel('P(2), W(3)');

To train the network, first override the default number of epochs, and then train the network. When it is finished, replot the input vectors '+' and the competitive neurons' weight vectors 'o'. Red = class 1, Cyan = class 2.

net.trainParam.epochs=150;
net.trainParam.show=Inf;
net=train(net,P,T);

cla;
plotvec(P,C);
hold on;
plotvec(net.IW{1}',vec2ind(net.LW{2}),'o');

Now use the LVQ network as a classifier, where each neuron corresponds to a different category. Present the input vector [0.2; 1]. Red = class 1, Cyan = class 2.

p = [0.2; 1];
a = vec2ind(sim(net,p))
a =

     2