Here’s a simple algorithm to produce Self-organizing neural networks (SONN) in 2D clustering problems with a simple decremented gain.

Number of clusters of input data *x* represented by , and is the number of features in each cluster. To represent the amount of change in the weights as a function of the distance from the center cluster , here I use window function , and the goal is to decrement the gain for updating the weights at next step iteration.

**Step 1** : set the weight in all clusters to random values :

,

for ; ; and

Set the initial gain .

**Step 2** : For each input pattern

where ,

(a). Identify the cluster that is closest to to the *k*-th input :

.

(b). Update the weights of the clusters in the neighborhood of cluster according to the rule :

, for ,

Where is window function.

**Step 3** : Decrement the gain term used for adapting the weight :

,

where is the learning rate.

**Step 4** : Repeat by going back to step 2 until convergence.

For the similar 1D SONN algorithm see here.

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