The authors explore the effect of different topologies on properties of self-organizing maps (SOM). They suggest several diagnostics for measuring topology-induced errors in SOM and use these in a comparison of four different topologies. The results show that SOM is less sensitive to localized irregularities in the network structure than the literature may otherwise suggest. Further, the results support the use of spherical topologies as a solution to the boundary problem in traditional SOM.
BoudjemaiF., EnbergP. B., and PostaireJ. G.. 2003. Surface modeling by using self organizing maps of Kohonen. In Systems, Man and Cybernetics, 2003. IEEE International Conference, vol. 3, 2418–23.
2.
HarrisJ. M, HirstJ. L., and MossinghoM. J.. 2000. Combinatorics and graph theory.New York: Springer.
3.
ItoM., MiyoshiT., and MasuyamaH.. 2000. The characteristics of the torus self organizing map. In Proceedings of 6th International Conference on Soft Computing (IIZUKA 2000), vol. A-7-2, 239–44, Iizuka, Fukuoka, Japan.
4.
KohonenT. (2001). Self-organizing maps, 3rd ed.Berlin and New York: Springer.
5.
LiX., GasteigerJ., and ZupanJ.. 1993. On the topology distortion in self-organizing feature maps.Biological Cybernetics70: 189–98.
6.
NishioH., Altaf-Ul-AminM., KurokawaK., and KanayaS.. 2006. Spherical SOM and arrangement of neurons using helix on sphere.IPSJ Digital Courier2: 133–7.
7.
RakhmanovE. A., SaffE. B., and ZhouY. M.. 1994. Minimal discrete energy on the sphere.Mathematical Research Letters1: 647–62.
8.
ReyS. J.2004. Spatial analysis of regional economic growth, inequality and change. In Spatially integrated social science, ed. GoodchildM. F., and JanelleD. G., 280–99. Oxford: Oxford University Press.
9.
RitterH.1999. Self-organizing maps on non-euclidean spaces. In Kohonen Maps, ed. OjaE., and KaskiS., 97–110. Amsterdam: Elsevier.
10.
SangoleA., and KnopfG. K.. 2003. Visualization of randomly ordered numeric data sets using spherical self-organizing feature maps.Computers & Graphics27: 963–76.
11.
SkupinA., and AgarwalP.. 2008. Introduction: What is a self-organizing map? In Self-organising maps: Applications in Geographic Information Science, ed. AgarwalP., and SkupinA., Chichester, UK: Wiley.
12.
WuY., and TakatsukaM.. 2005. Geodesic self-organizing map. In Proceedings of SPIE, vol. 5669, volume 5669 of Visualization and Data Analysis 2005, ed. R. F. Erbacher, J. C. Roberts, M. T. Grohn, and K. Borner, 21–30. Bellingham, WA: SPIE.
13.
WuY., and TakatsukaM.. 2006. Spherical self-organizing map using efficient indexed geodesic data structure.Neural Networks19: 900–10.
