A dimension range representation (DRR) measure for self-organizing maps

A common tool in exploratory data analysis, the self-organizing map, or SOM, is used for clustering and visualisation to discover patterns in large, high-dimensional data sets. The output map may be interpreted to gain an understanding of the structure of the original data set, correlations between variables, and the characteristics the clusters formed by placing the data on the map. However, if the map does not represent all dimensions of the data in an informative way, map interpretation may be misleading. Currently there is no measure of how well a SOM represents each dimension of a data set, and therefore how descriptive the map vectors are of the full structure of the data they represent. A dimension range representation (DRR) measure is proposed to quantify how well represented each dimension of the data set is by the map vectors of the SOM. This can be used to choose between different map size and shape options that could potentially represent a specific data set. Through examples, it is demonstrated how the DRR measure is used to inform the choice of map size and shape, leading to more informative insight into the original data set through examination of the output map.