Gravitational Clustering of the Self-Organizing Map

Data clustering is the fundamental data analysis method, widely used for solving problems in the field of machine learning. Numerous clustering algorithms exist, based on various theories and approaches, one of them being the well-known Kohonen's self-organizing map (SOM). Unfortunately, after training the SOM there is no explicitly obtained information about clusters in the underlying data, so another technique for grouping SOM units has to be applied afterwards. In this paper, a contribution towards clustering of the SOM is presented, employing principles of Gravitational Law. On the first level of the proposed algorithm, SOM is trained on the input data and prototypes are extracted. On the second level, each prototype acts as a unit-mass point in a feature space, in which presence of gravitational force is simulated, exploiting information about connectivity gained on the first level. The proposed approach is capable of discovering complex cluster shapes, not only limited to the spherical ones, and is able to automatically determine the number of clusters. Experiments with synthetic and real data are conducted to show performance of the presented method in comparison with other clustering techniques.