Accelerating the pace of engineering and science

# Documentation

### Contents

• Function Fitting and Approximation
• Pattern Recognition and Classification
• Clustering
• Dynamic Modeling and Prediction
• Control Systems and Simulink
• Self-organizing Networks
• Adaptive Linear Filters
• Radial Basis Networks
• LVQ Networks
• Simple Applications
• Hopfield Networks
• Perceptrons
• Other Examples

## Learning Vector Quantization

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

Let X 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.

```x = [-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(x,c)
title('Input Vectors');
xlabel('x(1)');
ylabel('x(2)');
```

Here LVQNET creates an LVQ layer with four hidden neurons and a learning rate of 0.1. The network is then configured for inputs X and targets T. (Configuration normally an unnecessary step as it is done automatically by TRAIN.)

```net = lvqnet(4,0.1);
net = configure(net,x,t);
```

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('x(1), w(1)');
ylabel('x(2), w(2)');
```

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=train(net,x,t);

cla;
plotvec(x,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.

```x1 = [0.2; 1];
y1 = vec2ind(net(x1))
```
```y1 =

2

```
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