Grid topologies for the self-organizing map

• The topologies of the map lattice for SOMs have rarely been researched.
• This work studies alternative map topologies to those used in previous literature.
• The theory of tessellations is used to obtain the alternative topologies.
• The alternative topologies outperform the classical ones in several tasks.
• A theory of SOFM topologies is developed.

The original Self-Organizing Feature Map (SOFM) has been extended in many ways to suit different goals and application domains. However, the topologies of the map lattice that we can found in literature are nearly always square or, more rarely, hexagonal. In this paper we study alternative grid topologies, which are derived from the geometrical theory of tessellations. Experimental results are presented for unsupervised clustering, color image segmentation and classification tasks, which show that the differences among the topologies are statistically significant in most cases, and that the optimal topology depends on the problem at hand. A theoretical interpretation of these results is also developed.