SOM of SOMs

This paper proposes an extension of the self-organizing map (SOM), in which the mapping objects themselves are self-organizing maps. Thus a “SOM of SOMs” is presented, which we refer to as a SOM2. A SOM2 has a hierarchical structure consisting of a single parent SOM and a set of child SOMs. Each child SOM is trained to represent the distribution of a data class in a manifold, while the parent SOM generates a self-organizing map of the group of manifolds modeled by the child SOMs. Thus a SOM2 is an architecture that organizes a product manifold represented as (child SOM) ×× (parent SOM). Such a product manifold is called a fiber bundle in terms of the topology. This extension of a SOM is easily generalized to any combination of SOM families, including cases of neural gas (NG) in which, for example, “ NG2 (=NG×NG) as an NG of NGs” and “NG××SOM as a SOM of NGs” are possible. Furthermore, a SOM2 can be extended to a SOMn, such as SOM3=SOM×SOM×SOMSOM3=SOM×SOM×SOM defined as a “SOM of SOM2”. In this paper, the algorithms for the SOM2 and its variations are introduced, and some simulation results are reported.