Skip to main content
SpringerLink
Log in

Fractal initialization for high-quality mapping with self-organizing maps

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Initialization of self-organizing maps is typically based on random vectors within the given input space. The implicit problem with random initialization is the overlap (entanglement) of connections between neurons. In this paper, we present a new method of initialization based on a set of self-similar curves known as Hilbert curves. Hilbert curves can be scaled in network size for the number of neurons based on a simple recursive (fractal) technique, implicit in the properties of Hilbert curves. We have shown that when using Hilbert curve vector (HCV) initialization in both classical SOM algorithm and in a parallel-growing algorithm (ParaSOM), the neural network reaches better coverage and faster organization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Abdulkader H, Ibnkahla M (2000) Convergence properties of self-organizing maps applied for communication channel equalization. In: IEEE international conference on acoustics, speech and signal processing, pp 3502–3505

  2. Bai Y, Zhang W, Jin Z (2006) A new self-organizing maps strategy for solving the traveling salesman problem, chaos, solutions and fractals. Elsevier, Amsterdam, pp 1082–1089

    Google Scholar 

  3. Bear M, Connors B, Paradiso M (2006) Neuroscience, exploring the brain, 3rd edn. Lippincott, Williams, and Wilkins publishing, USA

  4. Bechtel W, Abrahamsen A (2001) Connectionism and the mind, 2nd edn. Blackwell publishers, Oxford

    Google Scholar 

  5. Changeux JP (1983) L’Homme Neuronal, Fayard

  6. Churchland P, Sejnowski T (1992) The computational brain. MIT Press, Cambridge

    Google Scholar 

  7. Deaton R, Tang L, Reddick WE (1994) Fractal analysis of magnetic resonance images of the brain. In: International conference of IEEE engineering in medicine and biology, pp 616–617

  8. Erwin E, Obermayer K, Schulten K (1997) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47–55

    Article  Google Scholar 

  9. Fritzke B (1994) Growing cell structures—a self-organizing network for unsupervised and supervised learning. Neural Netw 7(9):1441–1460

    Article  Google Scholar 

  10. Fritzke B (1995) Growing grid—a self-organizing network with constant neighborhood range and adaptation strength. Neural Process Lett 2(5):9–13

    Article  Google Scholar 

  11. Hammond J, MacLean D, Valova I (2006) A parallel implementation of a growing SOM promoting independent neural networks over distributed input space. In: Proceedings international joint conference on neural networks, pp 1937–1944

  12. Haykin S (1999) Neural networks: a comprehensive foundation, 2nd edn. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  13. Hollmen J, Tresp V, Simula O (2000) A learning vector quantization algorithm for probabilistic models. EUSIPCO II:721–724

    Google Scholar 

  14. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948

  15. Kohonen T (1995) Self-organizing maps, 2nd edn. Springer, New York

    Google Scholar 

  16. Lagus K, Kaski S, Kohonen T (2004) Mining massive document collections by the WEBSOM method. Inf Sci 163(1–3):135–156

    Article  Google Scholar 

  17. MacLean D, Valova I (2007) Parallel growing SOM monitored by genetic algorithm. In: Proceedings international joint conference on neural networks, pp 1697–1702

  18. Mandelbrot BB (1982) The fractal geometry of nature, chap 7, harnessing the Peano Monster curves. W. H. Freeman, San Francisco

    Google Scholar 

  19. Peitgen HO, Jurgens H, Saupe D (2004) Chaos and fractals: new frontiers of science. Springer, New York

    MATH  Google Scholar 

  20. Polani D (2002) Measures for the organization of self-organizing maps. In: Seiffert U, Jain LC (eds) Self-organizing neural networks. Physica-Verlag, Wurzburg, pp 13–44

    Google Scholar 

  21. deRidder D, Duin RPW (1997) Sammon’s mapping using neural networks: a comparison. Pattern Recogn Lett 18:1307–1316

    Article  Google Scholar 

  22. Ritter H, Schulter K (1988) Kohonen’s self-organizing feature maps: exploring their computational capabilities. In: Proceedings of IEEE international conference on neural networks, vol 1, pp 109–116

  23. Sagan H (1994) Space-filling curves. Springer, New York

    MATH  Google Scholar 

  24. Sammon JW (1969) A nonlinear mapping for data structure analysis. IEEE Trans Comput C-18:401–409

    Article  Google Scholar 

  25. Su MC, Chang HT (2000) Fast self-organizing feature map algorithm. IEEE Trans Neural Netw 11:721–733

    Article  Google Scholar 

  26. Su MC, Liu TK, Chang HT (1999) An efficient initialization scheme for the self-organizing feature map algorithm. In: Proceedings IJCNN, pp 1906–1910

  27. Torgerson WS (1952) Multidimensional scaling I—theory and method. Psychometrika 17:401–419

    Article  MATH  MathSciNet  Google Scholar 

  28. Valova I, Szer D, Gueorguieva N, Buer A (2005) A parallel growing architecture for self-organizing maps with unsupervised learning. Neurocomputing 68:177–195

    Article  Google Scholar 

  29. Valova I, Beaton D, Buer A, MacLean D (2008) CQoCO: a Measure for Comparative Quality of Coverage and organization for Self-Organizing Maps, in review for Neural Networks, submitted April 2008

  30. Zhang WD, Bai YP, Hu HP (2006) The incorporation of an efficient initialization method and parameter adaptation using self-organizing maps to solve TSP, Applied Mathematics and Computation, Elsevier, pp 603–623

Download references

Author information

Authors and Affiliations

  1. Computer and Information Science, University of Massachusetts Dartmouth, 285 Old Westport Rd, North Dartmouth, MA, 02747, USA

    Iren Valova, Derek Beaton, Alexandre Buer & Daniel MacLean

Authors
  1. Iren Valova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Derek Beaton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexandre Buer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Daniel MacLean
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iren Valova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Valova, I., Beaton, D., Buer, A. et al. Fractal initialization for high-quality mapping with self-organizing maps. Neural Comput & Applic 19, 953–966 (2010). https://doi.org/10.1007/s00521-010-0413-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-010-0413-5

Keywords

Search

Navigation