A Consideration on the multi-dimensional topology in Self-Organizing Maps

The 1-dimensional topological network (line) and 2-dimensional topological network (2D-plane) of self-organizing Maps are well used for many applications. We propose the 3-dimensional topological self-organizing maps and give suggestion of an ability of more higher dimensional Maps. Since a compression ratio becomes low by 3-dimensional SOM as compared with 2-dimensional SOM, it may be able to leave more information on the original data. Research of 3- dimensional SOM is not popular. The main reasons are 1) The topology of units has various patterns and 2) The general-purpose topology which can be used in common with many data sets is not established. The data visualization technique of having been suitable for 3-dimensional SOM is proposed in this paper.