SOM of SOMs: An Extension of SOM from 'Map' to 'Homotopy'

摘要

This paper proposes an extension of an SOM called the "SOM of SOMs," or SOM~2, in which objects to be mapped are self-organizing maps. In SOM~2, each nodal unit of a conventional SOM is replaced by a function module of SOM. Therefore, SOM~2 can be regarded as a variation of a modular network SOM (mnSOM). Since each child SOM module in SOM~2 is trained to represent an individual map, the parent map in SOM~2 generates a self-organizing map representing the continuous change of the child maps. Thus SOM~2 is an extension of an SOM that generates a 'self-organizing homotopy' rather than a map. This extension of an SOM is easily generalized to the case of SOM~n, such that "SOM~3 as SOM of SOM~2s", corresponding to the n-th order of homotopy. This paper proposes a homotopy theory of SOM~2 with new simulation results.