A Two-dimensional Self-organizing Map

As in DEMOSM1, this self-organizing map will learn to represent different regions of the input space where input vectors occur. In this demo, however, the neurons will arrange themselves in a two-dimensional grid, rather than a line.

Copyright 1992-2002 The MathWorks, Inc. $Revision: 1.18 $ $Date: 2002/03/29 19:36:02 $

We would like to classify 1000 two-element vectors occuring in a rectangular shaped vector space.

P = rands(2,1000);
plot(P(1,:),P(2,:),'+r')

We will use a 5 by 6 layer of neurons to classify the vectors above. We would like each neuron to respond to a different region of the rectangle, and neighboring neurons to respond to adjacent regions. We create a layer of 30 neurons spread out in a 5 by 6 grid:

net = newsom([0 1; 0 1],[5 6]);

We can visualize the network we have just created with PLOTSOM.

Each neuron is represented by a red dot at the location of its two weights. Initially all the neurons have the same weights in the middle of the vectors, so only one dot appears.

plotsom(net.iw{1,1},net.layers{1}.distances)

Now we train the map on the 1000 vectors for 1 epoch and replot the network weights.

After training, note that the layer of neurons has begun to self-organize so that each neuron now classifies a different region of the input space, and adjacent (connected) neurons respond to adjacent regions.

net.trainParam.epochs = 1;
net = train(net,P);
plotsom(net.iw{1,1},net.layers{1}.distances)
TRAINR, Epoch 0/1
TRAINR, Epoch 1/1
TRAINR, Maximum epoch reached.

We can now use SIM to classify vectors by giving them to the network and seeing which neuron responds.

The neuron indicated by "a" responded with a "1", so p belongs to that class.

p = [0.5;0.3];
a = sim(net,p)
a =

  (19,1)        1