SOM of SOMs: An Extension of SOM from ‘Map’ to ‘Homotopy’
This paper proposes an extension of an SOM called the “SOM of SOMs,” or SOM2, in which objects to be mapped are self-organizing maps. In SOM2, each nodal unit of a conventional SOM is replaced by a function module of SOM. Therefore, SOM2 can be regarded as a variation of a modular network SOM (mnSOM). Since each child SOM module in SOM2 is trained to represent an individual map, the parent map in SOM2 generates a self-organizing map representing the continuous change of the child maps. Thus SOM2 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 “SOM3 as SOM of SOM2s”, corresponding to the n-th order of homotopy. This paper proposes a homotopy theory of SOM2 with new simulation results.
KeywordsData Vector Continuous Change Homotopy Theory Reference Vector Batch Learning
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