Abstract
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 SOMn, 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.
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Furukawa, T. (2006). SOM of SOMs: An Extension of SOM from ‘Map’ to ‘Homotopy’. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_106
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DOI: https://doi.org/10.1007/11893028_106
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46479-2
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