Topography-Enhanced BMU Search in Self-Organizing Maps

Abstract

Self-organizing maps (SOMs) have proven extremely useful because of their ability to provide a condensed representation of data. This is accomplished by creating a mapping from an often continuous data space to a discrete map grid, relationships on which ideally preserve much of the structure of the original data. When well-trained, Kohonen’s original SOM successfully preserves continuity in the mapping from the SOM grid to the data space. When the dimension of a map approximately matches the dimension of the data, or when the folding of a map into higher-dimensional data space is controlled, mapping algorithms can preserve the organization of the data more comprehensively. In these cases, the structure of the map grid may reflect the data structure at several levels of granularity, allowing the search for the best-matching unit (BMU) of the trained map to speed up significantly.