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 SOM(2). A SOM(2) 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 SOM(2) is an architecture that organizes a product manifold represented as (child SOM) x (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, " NG(2) (=NG x NG) as an NG of NGs" and "NG x SOM as a SOM of NGs" are possible. Furthermore, a SOM(2) can be extended to a SOM(n), such as SOM(3)=SOM x SOM x SOM defined as a "SOM of SOM(2)". In this paper, the algorithms for the SOM(2) and its variations are introduced, and some simulation results are reported.

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