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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 example, however, the neurons will arrange themselves in a two-dimensional grid, rather than a line.

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

X = rands(2,1000);
plot(X(1,:),X(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.

The network is configured to match the dimensions of the inputs. This step is required here because we will plot the initial weights. Normally configuration is performed automatically by TRAIN.

net = selforgmap([5 6]);
net = configure(net,X);

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

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.

plotsompos(net)

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,X);
plotsompos(net)

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 x belongs to that class.

x = [0.5;0.3];
y = net(x)
y =

     1
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0
     0

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