A growing self-organizing map (GSOM) is a growing variant of a self-organizing map (SOM). The GSOM was developed to address the issue of identifying a suitable map size in the SOM. It starts with a minimal number of nodes (usually 4) and grows new nodes on the boundary based on a heuristic. By using the value called Spread Factor (SF), the data analyst has the ability to control the growth of the GSOM. All the starting nodes of the GSOM are boundary nodes, i.e. each node has the freedom to grow in its own direction at the beginning. (Fig. 1) New Nodes are grown from the boundary nodes. Once a node is selected for growing all its free neighboring positions will be grown new nodes. The figure shows the three possible node growth options for a rectangular GSOM.
The algorithm The GSOM process is as follows:
Initialization phase: Initialize the weight vectors of the starting nodes (usually four) with random numbers between 0 and 1. Calculate the growth threshold ( G T {\displaystyle GT} ) for the given data set of dimension D {\displaystyle D} according to the spread factor ( S F {\displaystyle SF} ) using the formula G T = − D × ln ( S F ) {\displaystyle GT=-D\times \ln(SF)}
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![Growing self-organizing map: Approximation of a spiral with noise by 1D SOM (the upper row) and GSOM (the lower row) with 50 (the first column) and 100 (the second column) nodes. The Fraction of variance unexplained is: a) 4.68% (SOM, 50 nodes); b) 1.69% (SOM, 100 nodes); c) 4.20% (GSOM, 50 nodes); d) 2.32% (GSOM, 100 nodes). The initial approximation for SOM was equidistribution of nodes in a segment on the first principal component with the same variance as for the data set. The initial approximation for GSOM was the mean point.[1]](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/SOM_versus_GSOM.png/500px-SOM_versus_GSOM.png?utm_source=en.wikipedia.org&utm_campaign=parser&utm_content=thumbnail)
