Comparison of Flat SOM with Spherical SOM. A Case Study

Recently, several spherical self-organizing topographic maps have been introduced in the literature [1-4]. The maps are spherical or toroidal, and thus not bounded, as in the case of e.g. the traditional SOM algorithm and its many versions [5,6], and thus should not suffer from the border effect (border neurons are surrounded by less neurons). The emergence of these spherical maps raises a number of questions. Perhaps one of the most significant one is simply what advantage can one expect to gain from them as opposed to the traditional flat map model? To pursue a satisfactory answer to this fundamental question, the authors aim for a detailed comparison of models through visual and numerical analysis of a case study.