A Maximum-Likelihood Connectionist Model for Unsupervised Learning over Graphical Domains

  • Edmondo Trentin
  • Leonardo Rigutini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5768)


Supervised relational learning over labeled graphs, e.g. via recursive neural nets, received considerable attention from the connectionist community. Surprisingly, with the exception of recursive self organizing maps, unsupervised paradigms have been far less investigated. In particular, no algorithms for density estimation over graphs are found in the literature. This paper introduces first a formal notion of probability density function (pdf) over graphical spaces. It then proposes a maximum-likelihood pdf estimation technique, relying on the joint optimization of a recursive encoding network and a constrained radial basis functions-like net. Preliminary experiments on synthetically generated samples of labeled graphs are analyzed and tested statistically.


Density estimation unsupervised relational learning recursive network 


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  1. 1.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Duda, R., Hart, P.: Pattern Classification and Scene Analysis. Wiley, N.Y. (1973)zbMATHGoogle Scholar
  3. 3.
    Erdös, P., Rényi, A.: On random graphs. Publ. Math. Debrecen 6, 290–297 (1959)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Hammer, B., Micheli, A., Sperduti, A.: Universal approximation capability of cascade correlation for structures. Neural Computation 17(5), 1109–1159 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hammer, B., Micheli, A., Sperduti, A., Strickert, M.: Recursive self-organizing network models. Neural Networks 17(8-9), 1061–1085 (2004)CrossRefzbMATHGoogle Scholar
  6. 6.
    McLachlan, G.J., Basford, K.E. (eds.): Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York (1988)zbMATHGoogle Scholar
  7. 7.
    Sperduti, A., Starita, A.: Supervised neural networks for the classification of structures. IEEE Transactions on Neural Networks 8(3), 714–735 (1997)CrossRefGoogle Scholar
  8. 8.
    Trentin, E., Gori, M.: Robust combination of neural networks and hidden Markov models for speech recognition. IEEE Trans. on Neural Networks 14(6) (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Edmondo Trentin
    • 1
  • Leonardo Rigutini
    • 1
  1. 1.DII – Università di Siena, V. Roma56 SienaItaly

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