Analyzing the Behavior of the SOM through Wavelet Decomposition of Time Series Generated during Its Execution (original) (raw)

Abstract

Cluster analysis applications of the SOM require it to be sensible to features, or groupings, of different sizes in the input data. On the other hand, the SOM’s behavior while the organization process is taking place also exhibits regularities of different scales, such as periodic behaviors of different frequencies, or changes of different magnitudes in the weight vectors. A method based on the discrete wavelet transform is proposed for measuring the diversity of the scales of regularities, and this diversity is compared to the performance of the SOM. We argue that if this diversity of scales is high then the algorithm is more likely to detect differently sized features of data.

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References

  1. Kraaijveld, M., Mao, J., Jain, A.: A non-linear projection method based on Kohonen’s topology preserving maps. In: Proceedings of the 11th Int. Conf. on Pattern Recognition, pp. 41–45 (1992)
    Google Scholar
  2. Flexer, A.: On the Use of Self-Organizing Maps for Clustering and Visualization. Intelligent Data Analysis 5, 373–384 (2001)
    MATH Google Scholar
  3. Kohonen, T.: Self-organized formation of topologically correct feature maps. Biological Cybernetics 43, 59–69 (1982)
    Article MATH MathSciNet Google Scholar
  4. Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)
    Google Scholar
  5. Haykin, S.: Neural networks a comprehensive foundation, 2nd edn. Prentice-Hall, Englewood Cliffs (1999)
    MATH Google Scholar
  6. Mallat, S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Pattern Anal. and Machine Intell. 11(7), 674–693 (1989)
    Article MATH Google Scholar
  7. Haar, A.: Zur Theorie der orthogonalen Funktionensysteme. Math. Ann. 69, 331–371 (1910)
    Article MATH MathSciNet Google Scholar
  8. Walnut, D.: An Introduction to Wavelet Analysis. Birkhäuser, Basel (2001)
    Google Scholar
  9. Daubechies, I.: Ten Lectures on Wavelets Society for Industrial and Applied Mathematics (1992)
    Google Scholar
  10. Ogden, R.: Essential Wavelets for Statistical Applications and Data Analysis. Birkhauser, Basel (1997)
    MATH Google Scholar
  11. Kiviluoto, K.: Topology Preservation in Self-Organizing Maps. In: Proceedings of International Conference on Neural Networks, pp. 294–299 (1996)
    Google Scholar

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Authors and Affiliations

  1. Universidad Nacional Autónoma de México,
    Víctor Mireles
  2. Universidad Autónoma de la Ciudad de México,
    Antonio Neme

Authors

  1. Víctor Mireles
  2. Antonio Neme

Editor information

Véra Kůrková Roman Neruda Jan Koutník

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© 2008 Springer-Verlag Berlin Heidelberg

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Mireles, V., Neme, A. (2008). Analyzing the Behavior of the SOM through Wavelet Decomposition of Time Series Generated during Its Execution. In: Kůrková, V., Neruda, R., Koutník, J. (eds) Artificial Neural Networks - ICANN 2008. ICANN 2008. Lecture Notes in Computer Science, vol 5163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87536-9\_68

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