Advertisement

An Improved Adaptive Self-Organizing Map

  • Dominik Olszewski
  • Janusz Kacprzyk
  • Sławomir Zadrożny
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 634)

Abstract

We propose a novel adaptive Self-Organizing Map (SOM). In the introduced approach, the SOM neurons’ neighborhood widths are computed adaptively using the information about the frequencies of occurrences of input patterns in the input space. The neighborhood widths are determined independently for each neuron in the SOM grid. In this way, the proposed SOM properly visualizes the input data, especially, when there are significant differences in frequencies of occurrences of input patterns. The experimental study on real data, on three different datasets, verifies and confirms the effectiveness of the proposed adaptive SOM.

Keywords

Self-organizing map Adaptive self-organizing map Neighborhood width Gaussian kernel Data visualization 

Notes

Acknowledgments

This contribution is supported by the Foundation for Polish Science under International PhD Projects in Intelligent Computing. Project financed from The European Union within the Innovative Economy Operational Programme 2007–2013 and European Regional Development Fund.

References

  1. 1.
    Berglund, E., Sitte, J.: The parameterless self-organizing map algorithm. IEEE Trans. Neural Netw. 17(2), 305–316 (2006)CrossRefGoogle Scholar
  2. 2.
    Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent Dirichlet allocation. J. Mach. Learn. Res. 3, 993–1022 (2003)zbMATHGoogle Scholar
  3. 3.
    Chen, S., Zhou, Z., Hu, D.: Diffusion and growing self-organizing map: a nitric oxide based neural model. In: Advances in Neural Networks—ISNN 2004, Lecture Notes in Computer Science, vol. 3173 (2004)Google Scholar
  4. 4.
    Chengalvarayan, R., Deng, L.: HMM-based speech recognition using state-dependent, discriminatively derived transforms on mel-warped DFT features. IEEE Trans. Speech Audio Process. 2(3), 243–256 (1997)CrossRefGoogle Scholar
  5. 5.
    DeSieno, D.: Adding a conscience to competitive learning. In: Proceedings of the Second IEEE International Conference on Neural Networks (ICNN-88). vol. 1, pp. 117–124. IEEE (July 1988)Google Scholar
  6. 6.
    Frank, A., Asuncion, A.: UCI machine learning repository (2010), http://archive.ics.uci.edu/ml
  7. 7.
    Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000), http://circ.ahajournals.org/cgi/content/full/101/23/e215, circulation Electronic Pages
  8. 8.
    Haese, K., Goodhill, G.J.: Auto-SOM: recursive parameter estimation for guidance of self-organizing feature maps. Neural Comput. 13(3), 595–619 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inf. Syst. 17(2/3), 107–145 (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Handl, J., Knowles, J., Kell, D.B.: Computational cluster validation in post-genomic data analysis. Bioinformatics 21(15), 3201–3212 (2005)CrossRefGoogle Scholar
  11. 11.
    Heskes, T.: Self-organizing maps, vector quantization, and mixture modeling. IEEE Trans. Neural Netw. 12(6), 1299–1305 (2001)CrossRefGoogle Scholar
  12. 12.
    van Hulle, M.M.: Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization. Wiley, New York (2000)Google Scholar
  13. 13.
    Iglesias, R., Barro, S.: SOAN: self organizing with adaptive neighborhood neural network. In: Mira, J., Sánchez-Andrés, J. (eds.) Foundations and Tools for Neural Modeling. Lecture Notes in Computer Science, vol. 1606, pp. 591–600. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Ippoliti, D., Zhou, X.: A-GHSOM: an adaptive growing hierarchical self organizing map for network anomaly detection. J. Parallel Distrib. Comput. 72(12), 1576–1590 (2012)CrossRefGoogle Scholar
  15. 15.
    Kohonen, T.: Self-Organizing Maps. 3rd edn, Springer, Heidelberg (2001)Google Scholar
  16. 16.
    Kohonen, T.: Essentials of the self-organizing map. Neural Netw. 37, 52–65 (2013)CrossRefGoogle Scholar
  17. 17.
    Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cybern. 43(1), 59–69 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kohonen, T.: The self-organizing map. Proc. IEEE 28, 1464–1480 (1990)CrossRefGoogle Scholar
  19. 19.
    Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)CrossRefGoogle Scholar
  20. 20.
    van der Maaten, L., Hinton, G.E.: Visualizing data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008)zbMATHGoogle Scholar
  21. 21.
    Martín-Merino, M., Muñoz, A.: Visualizing asymmetric proximities with SOM and MDS models. Neurocomputing 63, 171–192 (2005)CrossRefGoogle Scholar
  22. 22.
    Mulier, F., Cherkassky, V.: Self-organization as an iterative Kernel smoothing process. Neural Comput. 7(6), 1165–1177 (1995)CrossRefGoogle Scholar
  23. 23.
    Nybo, K., Venna, J., Kaski, S.: The self-organizing map as a visual neighbor retrieval method. In: Proceedings of the 6th International Workshop on Self-Organizing Maps (WSOM 2007). pp. 1–8 (2007)Google Scholar
  24. 24.
    Olszewski, D.: An experimental study on asymmetric self-organizing map. In: Yin, H., Wang, W., Rayward-Smith, V. (eds.) Intelligent Data Engineering and Automated Learning—IDEAL 2011. Lecture Notes in Computer Science, vol. 6936, pp. 42–49 (2011)Google Scholar
  25. 25.
    Olszewski, D.: \(k\)-Means clustering of asymmetric data. In: Corchado, E., Snášel, V., Abraham, A., Woźniak, M., Grana, M., Cho, S.B. (eds.) Hybrid Artificial Intelligent Systems. Lecture Notes in Computer Science, vol. 7208, pp. 243–254 (2012)Google Scholar
  26. 26.
    Olszewski, D.: Fraud detection using self-organizing map visualizing the user profiles. Knowl. Based Syst. 70, 324–334 (2014)CrossRefGoogle Scholar
  27. 27.
    Olszewski, D., Kacprzyk, J., Zadrożny, S.: Time series visualization using asymmetric self-organizing map. In: Tomassini, M., Antonioni, A., Daolio, F., Buesser, P. (eds.) Adaptive and Natural Computing Algorithms. Lecture Notes in Computer Science, vol. 7824, pp. 40–49. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  28. 28.
    Olszewski, D., Šter, B.: Asymmetric clustering using the alpha-beta divergence. Pattern Recog. 47(5), 2031–2041 (2014)CrossRefGoogle Scholar
  29. 29.
    Paatero, P., Tapper, U.: Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5(2), 111–126 (1994)CrossRefGoogle Scholar
  30. 30.
    Piastra, M.: Self-organizing adaptive map: Autonomous learning of curves and surfaces from point samples. Neural Netw. 41, 96–112 (2013)CrossRefzbMATHGoogle Scholar
  31. 31.
    Rauber, A., Merkl, D., Dittenbach, M.: The growing hierarchical self-organizing map: exploratory analysis of high-dimensional data. IEEE Trans. Neural Netw. 13(6), 1331–1341 (2002)CrossRefzbMATHGoogle Scholar
  32. 32.
    Ressom, H., Wang, D., Natarajan, P.: Adaptive double self-organizing maps for clustering gene expression profiles. Neural Netw. 16(5–6), 633–640 (2003)CrossRefGoogle Scholar
  33. 33.
    Segev, A., Kantola, J.: Identification of trends from patents using self-organizing maps. Expert Syst. Appl. 39(18), 13235–13242 (2012)CrossRefGoogle Scholar
  34. 34.
    Shah-Hosseini, H., Safabakhsh, R.: TASOM: A new time adaptive self-organizing map. IEEE Trans. Syst. Man Cybern. Part B Cybern. 33(2), 271–282 (2003)CrossRefGoogle Scholar
  35. 35.
    Shah-Hosseini, H.: Binary tree time adaptive self-organizing map. Neurocomputing 74(11), 1823–1839 (2011)CrossRefGoogle Scholar
  36. 36.
    Venna, J., Peltonen, J., Nybo, K., Aidos, H., Kaski, S.: Information retrieval perspective to nonlinear dimensionality reduction for data visualization. J. Mach. Learn. Res. 11, 451–490 (2010)MathSciNetzbMATHGoogle Scholar
  37. 37.
    Vesanto, J., Himberg, J., Alhoniemi, E., Parhankangas, J.: Self-organizing map in Matlab: the SOM Toolbox. In: Proceedings of the Matlab DSP Conference. pp. 35–40 (1999)Google Scholar
  38. 38.
    Vesanto, J., Himberg, J., Alhoniemi, E., Parhankangas, J.: SOM Toolbox for Matlab 5. Tech. Rep. Report A57, Helsinki University of Technology (2000)Google Scholar
  39. 39.
    Villmann, T., Claussen, J.C.: Magnification control in self-organizing maps and neural gas. Neural Comput. 18(2), 446–469 (2006)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Dominik Olszewski
    • 1
  • Janusz Kacprzyk
    • 2
  • Sławomir Zadrożny
    • 2
  1. 1.Faculty of Electrical EngineeringWarsaw University of TechnologyWarsawPoland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland

Personalised recommendations