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

  • Tetsuo Furukawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4232)


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.


Data Vector Continuous Change Homotopy Theory Reference Vector Batch Learning 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tetsuo Furukawa
    • 1
  1. 1.Kyushu Institute of TechnologyKitakyushuJapan

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