Assessing self-organization using order metrics

Self-Organizing Maps (SOM) are proving to be useful as data analysis and visualization tools because they can visually render the data analysis results in 2D or 3D, and do not need category information for each input pattern. But this unsupervized nature of the training process makes it difficult to have separate training and test sets to determine the quality of the training process, which is done quite naturally for supervized Neural Network learning algorithms. In applications like data analysis, where there is little clue as to the way the SOM is supposed to look like after training, it is important to be able to assess the quality of the self-organization process independent of the application, and without need for category information. The Average Unit Disorder has been used to assess the quality of the ordering of a self-organized map. It is shown here that this same order metric can be used to assess the quality of the self-organization process itself. Based on this order metric, it can be determined whether the SOM has adequately learned, whether the parameters used to train the SOM have been correctly specified, and whether the SOM variant used is well-suited to the specific problem at hand.