Self-Organizing Maps for Structured Domains: Theory, Models, and Learning of Kernels

  • Fabio Aiolli
  • Giovanni Da San Martino
  • Markus Hagenbuchner
  • Alessandro Sperduti
Part of the Studies in Computational Intelligence book series (SCI, volume 247)


Self-Organizing Maps (SOMs) are a form of Machine Learning methods which are popularly applied as a tool to either cluster vectorial information, or to produce a topology preserving projection of high dimensional data vectors onto a low dimensional (often 2-dimensional) display space [20]. A SOM is generally trained unsupervised. The computational complexity of the underlying algorithms grows linearly with the size and number of inputs, which renders the SOM suitable for data mining tasks. The standard SOM algorithm is defined on input domains involving fixed sized data vectors. It is however recognized that many problem domains are naturally represented by structured data which are more complex than fixed sized vectors. Just to give some examples, in speech recognition, data is available in the form of variable length temporal vectors, while in Chemistry data is most naturally represented through molecular graphs.Moreover, numerous data mining tasks provide structural information which may be important to consider during the processing. For example, document mining in the world wide web involves both inter-document structure due to the formatting or hypertext structure, and intra-document structure due to hyperlink or reference dependencies. Note that any model capable of dealing with graphs can be used also in applications involving vectors, sequences, and trees, since these are special cases of graphs.


Kernel Function Root Node Leaf Node Data Label Winning Neuron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Asai, T., Abe, K., Kawasoe, S., Arimura, H., Sakamoto, H., Arikawa, S.: Efficient substructure discovery from large semi-structured data. In: Proc. Second SIAM Int. Conf. Data Mining (SDM 2002), pp. 158–174 (2002)Google Scholar
  2. 2.
    Bloehdorn, S., Moschitti, A.: Structure and semantics for expressive text kernels. In: Proceedings of the Sixteenth ACM conference on Information and Knowledge Management (CIKM 2007), pp. 861–864 (2007)Google Scholar
  3. 3.
    Collins, M., Duffy, N.: New ranking algorithms for parsing and tagging: Kernels over discrete structures, and the voted perceptron. In: Proceedings of the 40th Annual Meeting on Association for Computational Linguistics (ACL 2002), pp. 263–270 (2002)Google Scholar
  4. 4.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)zbMATHGoogle Scholar
  5. 5.
    Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995)zbMATHGoogle Scholar
  6. 6.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University Press, Cambridge (2000)Google Scholar
  7. 7.
    Denoyer, L., Gallinari, P.: Report on the xml mining track at inex 2005 and inex 2006: categorization and clustering of xml documents. SIGIR Forum 41(1), 79–90 (2007)CrossRefGoogle Scholar
  8. 8.
    Gartner, T.: A survey of kernels for structured data. ACM SIGKDD Explorations Newsletter 5(1), 49–58 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Gori, M., Hagenbuchner, M., Tsoi, A.C.: The traffic policeman benchmark. Technical report, University of Wollongong, Australia (December 1998)Google Scholar
  10. 10.
    Günter, S., Bunke, H.: Self-organizing map for clustering in the graph domain. Pattern Recognition Letters 23(4), 405–417 (2002)zbMATHCrossRefGoogle Scholar
  11. 11.
    Guyon, I.: An introduction to variable and feature selection. Journal of Machine Learning Research 3, 1157–1182 (2003)zbMATHCrossRefGoogle Scholar
  12. 12.
    Hagenbuchner, M., Sperduti, A., Tsoi, A.C.: Contextual processing of graphs using self-organizing maps. In: Proceedings of the 13th European Symposium on Artificial Neural Networks (ESANN 2005), pp. 399–404 (2005)Google Scholar
  13. 13.
    Hagenbuchner, M., Sperduti, A., Tsoi, A.C.: Contextual self-organizing maps for structured domains. In: Proceedings of the Workshop on Relational Machine Learning, pp. 46–55 (2005)Google Scholar
  14. 14.
    Hagenbuchner, M., Tsoi, A.C., Sperduti, A.: A supervised self-organising map for structured data. In: Allison, N., Yin, H., Allison, L., Slack, J. (eds.) WSOM 2001 - Advances in Self-Organising Maps, pp. 21–28. Springer, Heidelberg (2001)Google Scholar
  15. 15.
    Hagenbuchner, M.: Unsupervised learning of data-structures. An expository overview and comments. Technical report, University of Wollongong, Australia, and University of Siena, Italy (1999), Scholar
  16. 16.
    Hagenbuchner, M., Tsoi, A.C.: A benchmark for testing adaptive systems on structured data. In: Proceedings of the 7th European Symposium on Artificial Neural Networks (ESANN 1999), pp. 63–68 (1999)Google Scholar
  17. 17.
    Hammer, B., Micheli, A., Sperduti, A.: Universal approximation capability of cascade correlation for structures. Neural Comput. 17(5), 1109–1159 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kashima, H.: Machine Learning Approaches for Structured Data. PhD thesis, Graduate School of Informatics, Kyoto University, Japan (2007)Google Scholar
  19. 19.
    Kashima, H., Koyanagi, T.: Kernels for semi-structured data. In: Proceedings of the Nineteenth International Conference on Machine Learning (ICML 2002), pp. 291–298 (2002)Google Scholar
  20. 20.
    Kohonen, T.: Self-Organisation and Associative Memory, 3rd edn. Springer, Heidelberg (1990)Google Scholar
  21. 21.
    Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995)Google Scholar
  22. 22.
    Lodhi, H., Saunders, C., Shawe-Taylor, J., Cristianini, N., Watkins, C.: Text classification using string kernels. Journal of Machine Learning Research 2, 419–444 (2002)zbMATHCrossRefGoogle Scholar
  23. 23.
    Moschitti, A.: A study on convolution kernel for shallow semantic parsing. In: Proceedings of the 42nd Annual Meeting on Association for Computational Linguistics (ACL 2004), pp. 335–342 (2004)Google Scholar
  24. 24.
    Suzuki, J., Isozaki, H.: Sequence and tree kernels with statistical feature mining. In: Weiss, Y., Schölkopf, B., Platt, J. (eds.) Advances in Neural Information Processing Systems, vol. 18, pp. 1321–1328. MIT Press, Cambridge (2006)Google Scholar
  25. 25.
    Trentini, F., Hagenbuchner, M., Sperduti, A., Scarselli, F., Tsoi, A.C.: A self-organising map approach for clustering of xml documents. In: IEEE World Congress on Computational Intelligence, WCCI 2006, Vancouver, Canada, pp. 1805–1812. IEEE Press, Los Alamitos (2006)Google Scholar
  26. 26.
    van Hulle, M.: Faithful Representations and Topographic Maps. John Wiley, New York (2000)Google Scholar
  27. 27.
    Vishwanathan, S.V.N., Smola, A.J.: Fast kernels for string and tree matching. In: Neural Information Processing Systems, NIPS 2002, pp. 569–576 (2002)Google Scholar
  28. 28.
    Watkins, C.: Dynamic alignment kernels. In: Advances in Large Margin Classifiers, pp. 39–50. MIT Press, Cambridge (1999)Google Scholar
  29. 29.
    Wettschereck, D., Aha, D.W., Mohri, T.: A review and empirical evaluation of feature weighting methods for a class of lazy learning algorithms. Artificial Intelligence Review 11, 273–314 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Fabio Aiolli
    • 1
  • Giovanni Da San Martino
    • 1
  • Markus Hagenbuchner
    • 2
  • Alessandro Sperduti
    • 1
  1. 1.Dept. of Pure and Applied MathematicsPadua UniversityPaduaItaly
  2. 2.School of Computer Science and Software Engineering, Faculty of InformaticsUniversity of WollongongWollongongAustralia

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