Maps of Other Shapes

Two-dimensional maps are easy to visualize and are readily programmed. If the dataset is complicated, a larger two-dimensional map might be replaced 

A torus, which is the result of linking opposite sides of a two-dimensional rectangular SOM. 

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. 

There has been some recent work on the use of spherical SOMs. Just as a SOM shaped as a ring is one-dimensional (each node only has neighbors to the left and right), so a spherical SOM resembles a torus and is two-dimensional (neighbors to the left and right, and also to the top and bottom, but not above and below), so a spherical SOM should be faster in execution than a genuinely three-dimensional SOM. 

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