Eurofuse 2011 pp 257-268 | Cite as

Learning Valued Relations from Data

  • Willem Waegeman
  • Tapio Pahikkala
  • Antti Airola
  • Tapio Salakoski
  • Bernard De Baets
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 107)

Abstract

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval.

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References

  1. 1.
    Bowling, M., Fürnkranz, J., Graepel, T., Musick, R.: Machine learning and games. Machine learning 63(3), 211–215 (2006)CrossRefGoogle Scholar
  2. 2.
    Yamanishi, Y., Vert, J.-P., Kanehisa, M.: Protein network inference from multiple genomic data: a supervised approach. Bioinformatics 20, 1363–1370 (2004)CrossRefGoogle Scholar
  3. 3.
    Yang, Y., Bansal, N., Dakka, W., Ipeirotis, P., Koudas, N., Papadias, D.: Query by document. In: Proceedings of the Second ACM International Conference on Web Search and Data Mining, Barcelona, Spain, pp. 34–43 (2009)Google Scholar
  4. 4.
    Taskar, B., Wong, M., Abbeel, P., Koller, D.: Link prediction in relational data. In: Advances in Neural Information Processing Systems (2004)Google Scholar
  5. 5.
    De Raedt, L.: Logical and Relational Learning. Springer, Heidelberg (2009)Google Scholar
  6. 6.
    Vert, J.-P., Yamanishi, Y.: Supervised graph inference. In: Advances in Neural Information Processing Systems, vol. 17 (2005)Google Scholar
  7. 7.
    Xing, E., et al.: Distance metric learning with application to clustering with side information. In: Advances in Neural Information Processing Systems, vol. 16, pp. 521–528 (2002)Google Scholar
  8. 8.
    Hüllermeier, E., Fürnkranz, J.: Preference Learning. Springer, Heidelberg (2010)MATHGoogle Scholar
  9. 9.
    Geurts, P., Touleimat, N., Dutreix, M., d’Alché-Buc, F.: Inferring biological networks with output kernel trees. BMC Bioinformatics 8(2), S4 (2007)CrossRefGoogle Scholar
  10. 10.
    Doignon, J.-P., Monjardet, B., Roubens, M., Vincke, P.: Biorder families, valued relations and preference modelling. Journal of Mathematical Psychology 3030, 435–480 (1986)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Switalski, Z.: Transitivity of fuzzy preference relations - an empirical study. Fuzzy Sets and Systems 118, 503–508 (2000)MathSciNetCrossRefGoogle Scholar
  12. 12.
    De Baets, B., De Meyer, H., De Schuymer, B., Jenei, S.: Cyclic evaluation of transitivity of reciprocal relations. Social Choice and Welfare 26, 217–238 (2006)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Schölkopf, B., Smola, A.: Learning with Kernels, Support Vector Machines, Regularisation, Optimization and Beyond. The MIT Press, Cambridge (2002)Google Scholar
  14. 14.
    Ben-Hur, A., Noble, W.: Kernel methods for predicting protein-protein interactions. Bioinformatics 21(1), 38–46 (2005)CrossRefGoogle Scholar
  15. 15.
    De Schuymer, B., De Meyer, H., De Baets, B., Jenei, S.: On the cycle-transitivity of the dice model. Theory and Decision 54, 164–185 (2003)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fisher, L.: Rock, Paper, Scissors: Game Theory in Everyday Life. Basic Books, New York (2008)Google Scholar
  17. 17.
    Kerr, B., Riley, M., Feldman, M., Bohannan, B.: Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature 418, 171–174 (2002)CrossRefGoogle Scholar
  18. 18.
    Czárán, T., Hoekstra, R., Pagie, L.: Chemical warfare between microbes promotes biodiversity. Proceedings of the National Academy of Sciences 99(2), 786–790 (2002)CrossRefGoogle Scholar
  19. 19.
    Nowak, M.: Biodiversity: Bacterial game dynamics. Nature 418, 138–139 (2002)CrossRefGoogle Scholar
  20. 20.
    Kirkup, B., Riley, M.: Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428, 412–414 (2004)CrossRefGoogle Scholar
  21. 21.
    Károlyi, G., Neufeld, Z., Scheuring, I.: Rock-scissors-paper game in a chaotic flow: The effect of dispersion on the cyclic competition of microorganisms. Journal of Theoretical Biology 236(1), 12–20 (2005)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Reichenbach, T., Mobilia, M., Frey, E.: Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448, 1046–1049 (2007)CrossRefGoogle Scholar
  23. 23.
    Boddy, L.: Interspecific combative interactions between wood-decaying basidiomycetes. FEMS Microbiology Ecology 31, 185–194 (2000)CrossRefGoogle Scholar
  24. 24.
    Sinervo, S., Lively, C.: The rock-paper-scissors game and the evolution of alternative male strategies. Nature 340, 240–246 (1996)CrossRefGoogle Scholar
  25. 25.
    Waite, T.: Intransitive preferences in hoarding gray jays (Perisoreus canadensis). Journal of Behavioural Ecology and Sociobiology 50, 116–121 (2001)CrossRefGoogle Scholar
  26. 26.
    Luce, R., Suppes, P.: Preference, Utility and Subjective Probability. In: Handbook of Mathematical Psychology, pp. 249–410. Wiley, Chichester (1965)Google Scholar
  27. 27.
    Fishburn, P.: Nontransitive preferences in decision theory. Journal of Risk and Uncertainty 44, 113–134 (1991)CrossRefGoogle Scholar
  28. 28.
    Tversky, A.: In: Shafir, E. (ed.) Preference, Belief and Similarity. MIT Press, Cambridge (1998)Google Scholar
  29. 29.
    Gower, J., Legendre, P.: Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification 3, 5–48 (1986)MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Jäkel, F., Schölkopf, B., Wichmann, F.: Similarity, kernels, and the triangle inequality. Journal of Mathematical Psychology 52(2), 297–303 (2008)MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Switalski, Z.: General transitivity conditions for fuzzy reciprocal preference matrices. Fuzzy Sets and Systems 137, 85–100 (2003)MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    De Baets, B., De Meyer, H.: Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity. Fuzzy Sets and Systems 152, 249–270 (2005)MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    De Baets, B., Mesiar, R.: Metrics and T-equalities. Journal of Mathematical Analysis and Applications 267, 531–547 (2002)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Moser, B.: On representing and generating kernels by fuzzy equivalence relations. Journal of Machine Learning Research 7, 2603–2620 (2006)Google Scholar
  35. 35.
    Billot, A.: An existence theorem for fuzzy utility functions: A new elementary proof. Fuzzy Sets and Systems 74, 271–276 (1995)MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    Koppen, M.: Random Utility Representation of Binary Choice Probilities: Critical Graphs yielding Critical Necessary Conditions. Journal of Mathematical Psychology 39, 21–39 (1995)MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Fono, L., Andjiga, N.: Utility function of fuzzy preferences on a countable set under max-*-transitivity. Social Choice and Welfare 28, 667–683 (2007)MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Bodenhofer, U., De Baets, B., Fodor, J.: A compendium of fuzzy weak orders. Fuzzy Sets and Systems 158, 811–829 (2007)MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    Herbrich, R., Graepel, T., Obermayer, K.: Large margin rank boundaries for ordinal regression. In: Smola, A., Bartlett, P., Schölkopf, B., Schuurmans, D. (eds.) Advances in Large Margin Classifiers, pp. 115–132. MIT Press, Cambridge (2000)Google Scholar
  40. 40.
    Pahikkala, T., Tsivtsivadze, E., Airola, A., Järvinen, J., Boberg, J.: An efficient algorithm for learning to rank from preference graphs. Machine Learning 75(1), 129–165 (2009)CrossRefGoogle Scholar
  41. 41.
    Pahikkala, T., Waegeman, W., Tsivtsivadze, E., Salakoski, T., De Baets, B.: Learning intransitive reciprocal relations with kernel methods. European Journal of Operational Research 206, 676–685 (2010)MathSciNetMATHCrossRefGoogle Scholar
  42. 42.
    Pahikkala, T., Waegeman, W., Airola, A., Salakoski, T., De Baets, B.: Conditional ranking on relational data. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds.) ECML PKDD 2010. LNCS, vol. 6322, pp. 499–514. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Willem Waegeman
    • 1
  • Tapio Pahikkala
    • 2
  • Antti Airola
    • 2
  • Tapio Salakoski
    • 2
  • Bernard De Baets
    • 1
  1. 1.KERMIT, Department of Applied Mathematics, Biometrics and Process ControlGhent UniversityGhentBelgium
  2. 2.Department of Information Technology and the Turku Centre for Computer ScienceUniversity of TurkuTurkuFinland

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