SOM of SOMs: An Extension of SOM from ‘Map’ to ‘Homotopy’

機関リポジトリ HANDLE 被引用文献1件

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This paper proposes an extension of an SOM called the “SOM ofSOMs,” or SOM2, in which objects to be mapped are self-organizing maps. InSOM2, each nodal unit of a conventional SOM is replaced by a function moduleof SOM. Therefore, SOM2 can be regarded as a variation of a modular networkSOM (mnSOM). Since each child SOM module in SOM2 is trained to representan individual map, the parent map in SOM2 generates a self-organizing map representingthe continuous change of the child maps. Thus SOM2 is an extension ofan SOM that generates a ‘self-organizing homotopy’ rather than a map. This extensionof an SOM is easily generalized to the case of SOMn, such that “SOM3as SOM of SOM2s”, corresponding to the n-th order of homotopy. This paperproposes a homotopy theory of SOM2 with new simulation results.

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