Stress Measures in SOM Learning

  • Zuzana Krbcova
  • Jaromir Kukal
Keywords: SOM, metric space, stress function, optimization heuristics

Abstract

Various stress measures can be used in generalized version of Sammon’s mapping. Kohonen SOM with iterative or batch learning is a standard tool for data self-organization, too. Our method applies stress functions to pattern relationships in SOM and converts batch learning to discrete optimization task. Due to NP–completeness of SOM learning, optimization heuristics have to be used. Simulated annealing making use of Lévy flights is the recommended heuristics for this task.

References

Kohonen, T.: Self-Organizing Maps, third edn. Springer-Verlag, Berlin, Heidelberg, New York (2001)

Abe, T., Kanaya, S., Kinouchi, M., Kudo, Y., Mori, H., Matsuda, H., Carlos, D.C., and Ikemura, T.: Gene classification method based on batch-learning SOM. Genome Informatics 10, 314–315 (1999)

Kanaya, S., Kinouchi, M., Abe, T., Kudo, Y., Yamada, Y., Nishi, T.,Mori, H., Ikemura, T.: Analysis of codon usage diversity for bacterial genes with a self-organizing map (SOM): characterization of horizontally transferred genes with emphasis on the E. coli O157 genome. Gene 276, 89–99 (2001)

Mojzes M., Kukal J., Tran, V. Q., Jablonsky, J.: Performance comparison of heuristic algorithms via multi-criteria decision analysis. In: R. Matousek (ed.) Proceedings of 17th International Conference on Soft Computing – MENDEL 2011, pp. 244–251. Brno University of Technology, VUT Press, Brno (2011)

Sammon, J.W.: A nonlinear mapping for data structure analysis. IEEE Transaction on Computers C-18(5), 401–409 (1969)

Sun, J., Crowe, M., Fyfe, C.: Extending metric multidimensional scaling with Bregman divergences. Pattern Recognization 44(5), 1137–1154 (2011)

Sun, J., Fyfe, C., Crowe, M.: Extending Sammon mapping with Bregman divergences. Information Sciences 187(1), 72–92 (2012)

Kukal, J.: SOM in Metric Space. Neural Network World 14(6), 469–488 (2004)

Szu, H.: Fast simulated annealing. In: Denker J.S. (ed.) Proceeding of the AIP Conference on Neural Networks for Computing, pp. 420-425. American Institute of Physics, New York (1986)

Viswanathan, G.M., Raposo, E.P., Da Luz, M.G.E.: L´evy flights and superdiffusion in the context of biological encounters and random searches. Physics of Life Reviews 5(3), 133–150 (2008)

Feoktistov, V.: Differential evolution, In Search of Solutions. Springer, Boston, MA (2006)

Published
2018-06-01
How to Cite
[1]
KrbcovaZ. and KukalJ. 2018. Stress Measures in SOM Learning. MENDEL. 24, 1 (Jun. 2018), 107-112. DOI:https://doi.org/10.13164/mendel.2018.1.107.
Section
Articles