Examples :: Self-Organizing and Learn. Vector Quant. Nets (Neural Network Toolbox)

Neural Network Toolbox

Examples

Two examples are described briefly below. You might try the demonstration scripts demosm1 and demosm2 to see similar examples.

One-Dimensional Self-Organizing Map

Consider 100 two-element unit input vectors spread evenly between 0° and 90°.

```
angles = 0:0.5*pi/99:0.5*pi;
```

Here is a plot of the data.

```
P = [sin(angles); cos(angles)];
```

We define a a self-organizing map as a one-dimensional layer of 10 neurons. This map is to be trained on these input vectors shown above. Originally these neurons will be at the center of the figure.

Of course, since all the weight vectors start in the middle of the input vector space, all you see now is a single circle.

As training starts the weight vectors move together toward the input vectors. They also become ordered as the neighborhood size decreases. Finally the layer adjusts its weights so that each neuron responds strongly to a region of the input space occupied by input vectors. The placement of neighboring neuron weight vectors also reflects the topology of the input vectors.

Note that self-organizing maps are trained with input vectors in a random order, so starting with the same initial vectors does not guarantee identical training results.

Two-Dimensional Self-Organizing Map

This example shows how a two-dimensional self-organizing map can be trained.

First some random input data is created with the following code.

```
P = rands(2,1000);
```

Here is a plot of these 1000 input vectors.

A two-dimensional map of 30 neurons is used to classify these input vectors. The two-dimensional map is five neurons by six neurons, with distances calculated according to the Manhattan distance neighborhood function mandist.

The map is then trained for 5000 presentation cycles, with displays every 20 cycles.

Here is what the self-organizing map looks like after 40 cycles.

The weight vectors, shown with circles, are almost randomly placed. However, even after only 40 presentation cycles, neighboring neurons, connected by lines, have weight vectors close together.

Here is the map after 120 cycles.

After 120 cycles, the map has begun to organize itself according to the topology of the input space which constrains input vectors.

The following plot, after 500 cycles, shows the map is more evenly distributed across the input space.

Finally, after 5000 cycles, the map is rather evenly spread across the input space. In addition, the neurons are very evenly spaced reflecting the even distribution of input vectors in this problem.

Thus a two-dimensional self-organizing map has learned the topology of its inputs' space.

It is important to note that while a self-organizing map does not take long to organize itself so that neighboring neurons recognize similar inputs, it can take a long time for the map to finally arrange itself according to the distribution of input vectors.

Training (learnsom) Learning Vector Quantization Networks