Self-organizing maps and boundary effects: quantifying the benefits of torus wrapping for mapping SOM trajectories
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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%.
KeywordsNeural nets Self-organizing maps Cluster analysis
This work was supported in part by an East Midlands Development Agency Innovation Fellowship.
- 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.Agarwal P, Skupin A (2008) Self-organizing maps: applications in geographic information science. Wiley, ChichesterGoogle Scholar
- 11.Doeboeck G, Kohonen T (1998) Visual explorations in finance with self-organizing maps. Springer, BerlinGoogle Scholar
- 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
- 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.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
- 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
- 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.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