The density-tracking self-organizing map

The self-organizing map (SOM) maps a distribution of vectors of arbitrary dimension into a lower-dimensional space (typically one or two) while maintaining a high degree of topological ordering (or neighborhood preservation). In an ideal SOM, each node would represent an equal number of input samples from the training set. In general, maps computed by Kohonen´s original SOM algorithm tend to use too many nodes to represent less dense regions of the input distribution, and not enough nodes to represent the more dense regions. The density-tracking self-organizing map (DSOM) is a new type of SOM that maps the density of the input distribution nearly exactly with very efficient use of network nodes. The DSOM also eliminates the requirement for any adjustable neighborhood function, which was previously considered essential to learning the topology of an input distribution. This paper explains the new algorithm and demonstrates its effectiveness with a mapping of normalized three-dimensional vectors into one dimension