Wraparound Maps

Although all the nodes in a SOM should be equivalent, nodes at the edge of the map are in a different environment than those near the middle. The 

This asymmetry may have an effect on the development of the map. If there are few examples of a particular class in the dataset or if the characteristics of some sample patterns are markedly different from the characteristics of most other samples, development of the map may be eased if these unusual samples find their way to the edge of the map where they have fewer neighbors. The remaining samples, which share a wider range of characteristics, then have the whole of the rest of the map to themselves and they can spread out widely to reveal the differences between them to the maximum degree permitted by the size of the map. 

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Wraparound in three dimensions is more complicated to program and very much more complicated to visualize. In one dimension, we accomplished wraparound by making neighbors of the two most extreme points in the map. In two dimensions, we needed to join outer edges of the map, but, in three dimensions, exterior faces at the extremes of the grid must be connected. The additional computational bookkeeping required to work in three dimensions may cancel out any extra flexibility that it provides in the evolution of a cubic or tetrahedral SOM. 

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