Advertisement

Pattern Analysis and Applications

, Volume 14, Issue 2, pp 139–148 | Cite as

Self-organizing maps and boundary effects: quantifying the benefits of torus wrapping for mapping SOM trajectories

  • N. J. MountEmail author
  • D. Weaver
Theoretical Advances

Abstract

In this study the impact of a planar and toroidal self-organizing map (SOM) configuration are investigated with respect to their impact on SOM trajectories. Such trajectories are an encoding of processes within an n-dimensional input data set and offer an important means of visualizing and analyzing process complexity in large n-dimensional problem domains. However, discontinuity associated with boundaries in the standard, planar SOM results in error that limits their analytical use. Previous studies have recommended the use of a toroidal SOM to reduce these errors, but fall short of a fully quantified analysis of the benefits that result. In this study, the comparative analysis of fifteen pairs of identically initiated and trained SOMs, of planar and toroidal configuration, allows the error in trajectory magnitude to be quantified and visualized; both within the SOM and data space. This offers an important insight into the impact of planar SOM boundaries that goes beyond the general, statistical measures of clustering efficacy associated with previous work. The adoption of a toroidal SOM can be seen to improve the distribution of error in the trajectory sets, with the specific spatial configuration of SOM neurons associated with the largest errors changing from those at the corners of the planar SOM to a more complex and less predictable pattern in the toroidal SOM. However, this improvement is limited to the smallest 60% of errors, with torus and planar SOMs performing similarly for the largest 40%.

Keywords

Neural nets Self-organizing maps Cluster analysis 

Notes

Acknowledgment

This work was supported in part by an East Midlands Development Agency Innovation Fellowship.

References

  1. 1.
    Kohonen T (2001) Self-organizing maps. Springer-Verlag, BerlinzbMATHGoogle Scholar
  2. 2.
    Mitra S, Pal SK (1994) Self-organizing neural networks as a fuzzy classifier. IEEE Trans Sys Man Cybern 24:385–399CrossRefGoogle Scholar
  3. 3.
    Kiang MY, Kulkarni U, Goul MK, Philippakis A, Chi RT, Turban E (1997) Improving the converging property of the self-organizing map network using a circular, wrap-around Kohonen layer. In: Proceedings of the 30th annual Hawaii international conference on neural networks, vol 5. IEEE Computer Science Press, Warsaw, pp 521–523Google Scholar
  4. 4.
    Agarwal P, Skupin A (2008) Self-organizing maps: applications in geographic information science. Wiley, ChichesterGoogle Scholar
  5. 5.
    Skific N, Francis JA, Cassano JJ (2009) Attribution of projected changes in atmospheric moisture transport in the arctic: a self-organizing map perspective. J Clim 22:4135–4153CrossRefGoogle Scholar
  6. 6.
    Foody GM (1999) Applications of the self-organizing feature map neural network in community data analysis. Environ Model 120:97–107CrossRefGoogle Scholar
  7. 7.
    Kuusela M, Lamsa JW, Malmi E, Mehtala P, Orava R (2010) Multivariate techniques for identifying diffractive interactions at the large Hadron collider. Int J Mod Phys A 25:1615–1647CrossRefGoogle Scholar
  8. 8.
    Faisal T, Taib MN, Ibrahim F (2010) Re-examination of risk criteria in dengue patients using the self-organizing map. Med Biol Eng Comput 43:293–301CrossRefGoogle Scholar
  9. 9.
    Moya-Anegon F, Herrero-Solana V, Jimenez-Contreras E (2006) A connectionist and multivariate approach to science maps: the SOM clustering and MDS applied to library science research and information. J Inf Sci 32:63–77CrossRefGoogle Scholar
  10. 10.
    Skupin A, Hagleman R (1995) Visualizing demographic trajectories with self-organizing maps. GeoInformatica 9:159–179CrossRefGoogle Scholar
  11. 11.
    Doeboeck G, Kohonen T (1998) Visual explorations in finance with self-organizing maps. Springer, BerlinGoogle Scholar
  12. 12.
    Skupin A (2008) Visualizing human movement in attribute space. In: Agarwal P, Skupin A (eds) Self-organizing maps: applications in geographic information science. Wiley, Chichester, pp 121–135Google Scholar
  13. 13.
    Lambin EF, Strahler AH (1994) Change-vector analysis in multitemporal space—a tool to detect and categorize land-cover change processes using high temporal-resolution satellite data. Remote Sens Environ 42:231–244CrossRefGoogle Scholar
  14. 14.
    Lo ZP, Bavarian B (1991) On the rate of convergence in topology-preserving neural networks. Biol Cybern 65:405–411MathSciNetCrossRefGoogle Scholar
  15. 15.
    Takahashi K, Sugakawa S (2004) Remarks on human posture classification using self-organizing maps. In: IEEE international conference on systems man and cybernetics, vol 3. The Hague, Netherlands, pp 2623–2628Google Scholar
  16. 16.
    Matsushita H, Nishio Y (2009) Network-structured particle swarm optimiser with various topology and its behaviours. In: Proc advances in self-organizing maps, lecture notes in computer science, vol 5629. pp 163–171Google Scholar
  17. 17.
    Ritter H (1999) Self-organizing maps in non-Euclidean spaces. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 97–109CrossRefGoogle Scholar
  18. 18.
    Sangloe A, Knopf GK (2002) Representing high-dimensional data sets as closed surfaces. Inf Vis 1:111–119CrossRefGoogle Scholar
  19. 19.
    Shumuker M, Schwarte F, Brüke A, Proschak E, Tanrikulu Y, Givehchi A, Scheiffele K, Schneider G (2007) SOMMER: self-organizing maps for education and research. J Mol Mod 13:225–228CrossRefGoogle Scholar
  20. 20.
    Wu Y, Takasuta M (2004) The geodesic self-organizing map and its error analysis. In: Proceedings of the 28th Australasian conference on computer science. Australian Computer Society, Darlinghurst, pp 343–351Google Scholar
  21. 21.
    Kiang MY, Kulkarni UR, St Louis R (2001) Circular/wrap-around self-organizing map networks: an empirical study in clustering and classification. J Oper Res Soc 52:93–101zbMATHCrossRefGoogle Scholar
  22. 22.
    Kulkarni UR, Kiang MY (1995) Dynamic grouping of parts in flexible manufacturing systems—a self-organizing neural networks approach. Eur J Oper Res 84:192–212zbMATHCrossRefGoogle Scholar
  23. 23.
    Kihato PK, Tokutaka H, Ohkita M, Fujimura K, Kotani K, Kurozawa Y, Maniwa Y (2008) Spherical and torus SOM approaches to metabolic syndrome evaluation. In: Lecture notes in computer science: neural information processing 4985/2004:274–284Google Scholar
  24. 24.
    Mount NJ, Weaver D (2008) Space–time trajectories in a planar and torus-based self-organizing map: the importance of eliminating boundary effects. In: Proceedings of the 16th annual geographic information science research UK conference, Manchester Metropolitan University, UK, pp 83–89Google Scholar
  25. 25.
    DeSieno D (1988) Adding a conscience to competitive learning. IEEE Int Conf Neural Netw 1:117–124CrossRefGoogle Scholar
  26. 26.
    Cavazos T (1999) Large scale circulation anomalies conductive to extreme precipitation events and derivation of daily rainfall in northeastern Mexico and southeastern Texas. J Climatol 12:1506–1523CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.School of GeographyUniversity of NottinghamNottinghamUK

Personalised recommendations