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Kohonen Self-Organizing Feature Maps

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Kohonen Self-Organizing Feature Maps

Self-Organizing Feature Maps(SOM) was developed by Dr. Teuvo Kohonen in 1982. Kohonen Self-Organizing feature map (KSOM) refers to a neural network, which is trained using competitive learning. Basic competitive learning implies that the competition process takes place before the cycle of learning. The competition process suggests that some criteria select a winning processing element. After the winning processing element is selected, its weight vector is adjusted according to the used learning law.
Feature mapping is a process which converts the patterns of arbitrary dimensionality into a response of one or two dimensions array of neurons. The network performing such a mapping is called feature map. The reason for reducing the higher dimensionality, the ability to preserve the neighbor topology.

Training Algorithm

Step 0: Initialize the weights with Random values and the learning rate

Step 1: Perform Steps 2-8 when stopping condition is false.

Step 2: Perform Steps 3-5 for each input vector x.

Step 3: Compute the square of the Euclidean distance, i.e., for each j = i to m,

$$D(j)={\displaystyle \underset{i=1}{\overset{n}{\sum <!--\; \sum \; -->}}{\displaystyle (x_i-<!--\; -\; -->w_{ij}{)}^2}}j=1tom$$

Step 4: Find the winning unit index J, so that D(J) is minimum.

Step 5: For all units j within a specific neighborhood of J and for all i, calculate the new weights:

$$w_{ij}(new)=w_{ij}(old)+\mathrm{\alpha <!--\; \alpha \; -->}[x_i-<!--\; -\; -->w_{ij}(old)]$$

Step 6: Update the learning rare a using the formula (t is timestamp)$$\mathrm{\alpha <!--\; \alpha \; -->}(t+1)=0.5\mathrm{\alpha <!--\; \alpha \; -->}(t)$$

Step 7: Reduce radius of topological neighborhood at specified time intervals.

Step 8: Test for stopping condition of the network.

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