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Learning Valued Relations from Data

  • Conference paper
Eurofuse 2011

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 107))

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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. Bowling, M., Fürnkranz, J., Graepel, T., Musick, R.: Machine learning and games. Machine learning 63(3), 211–215 (2006)

    Article  Google Scholar 

  2. Yamanishi, Y., Vert, J.-P., Kanehisa, M.: Protein network inference from multiple genomic data: a supervised approach. Bioinformatics 20, 1363–1370 (2004)

    Article  Google Scholar 

  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. Taskar, B., Wong, M., Abbeel, P., Koller, D.: Link prediction in relational data. In: Advances in Neural Information Processing Systems (2004)

    Google Scholar 

  5. De Raedt, L.: Logical and Relational Learning. Springer, Heidelberg (2009)

    Google Scholar 

  6. Vert, J.-P., Yamanishi, Y.: Supervised graph inference. In: Advances in Neural Information Processing Systems, vol. 17 (2005)

    Google Scholar 

  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. Hüllermeier, E., Fürnkranz, J.: Preference Learning. Springer, Heidelberg (2010)

    MATH  Google Scholar 

  9. Geurts, P., Touleimat, N., Dutreix, M., d’Alché-Buc, F.: Inferring biological networks with output kernel trees. BMC Bioinformatics 8(2), S4 (2007)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  11. Switalski, Z.: Transitivity of fuzzy preference relations - an empirical study. Fuzzy Sets and Systems 118, 503–508 (2000)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  13. Schölkopf, B., Smola, A.: Learning with Kernels, Support Vector Machines, Regularisation, Optimization and Beyond. The MIT Press, Cambridge (2002)

    Google Scholar 

  14. Ben-Hur, A., Noble, W.: Kernel methods for predicting protein-protein interactions. Bioinformatics 21(1), 38–46 (2005)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  16. Fisher, L.: Rock, Paper, Scissors: Game Theory in Everyday Life. Basic Books, New York (2008)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  19. Nowak, M.: Biodiversity: Bacterial game dynamics. Nature 418, 138–139 (2002)

    Article  Google Scholar 

  20. Kirkup, B., Riley, M.: Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428, 412–414 (2004)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  22. Reichenbach, T., Mobilia, M., Frey, E.: Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448, 1046–1049 (2007)

    Article  Google Scholar 

  23. Boddy, L.: Interspecific combative interactions between wood-decaying basidiomycetes. FEMS Microbiology Ecology 31, 185–194 (2000)

    Article  Google Scholar 

  24. Sinervo, S., Lively, C.: The rock-paper-scissors game and the evolution of alternative male strategies. Nature 340, 240–246 (1996)

    Article  Google Scholar 

  25. Waite, T.: Intransitive preferences in hoarding gray jays (Perisoreus canadensis). Journal of Behavioural Ecology and Sociobiology 50, 116–121 (2001)

    Article  Google Scholar 

  26. Luce, R., Suppes, P.: Preference, Utility and Subjective Probability. In: Handbook of Mathematical Psychology, pp. 249–410. Wiley, Chichester (1965)

    Google Scholar 

  27. Fishburn, P.: Nontransitive preferences in decision theory. Journal of Risk and Uncertainty 44, 113–134 (1991)

    Article  Google Scholar 

  28. Tversky, A.: In: Shafir, E. (ed.) Preference, Belief and Similarity. MIT Press, Cambridge (1998)

    Google Scholar 

  29. Gower, J., Legendre, P.: Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification 3, 5–48 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  30. Jäkel, F., Schölkopf, B., Wichmann, F.: Similarity, kernels, and the triangle inequality. Journal of Mathematical Psychology 52(2), 297–303 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Switalski, Z.: General transitivity conditions for fuzzy reciprocal preference matrices. Fuzzy Sets and Systems 137, 85–100 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  33. De Baets, B., Mesiar, R.: Metrics and T-equalities. Journal of Mathematical Analysis and Applications 267, 531–547 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Moser, B.: On representing and generating kernels by fuzzy equivalence relations. Journal of Machine Learning Research 7, 2603–2620 (2006)

    Google Scholar 

  35. Billot, A.: An existence theorem for fuzzy utility functions: A new elementary proof. Fuzzy Sets and Systems 74, 271–276 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  36. Koppen, M.: Random Utility Representation of Binary Choice Probilities: Critical Graphs yielding Critical Necessary Conditions. Journal of Mathematical Psychology 39, 21–39 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  38. Bodenhofer, U., De Baets, B., Fodor, J.: A compendium of fuzzy weak orders. Fuzzy Sets and Systems 158, 811–829 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

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Waegeman, W., Pahikkala, T., Airola, A., Salakoski, T., De Baets, B. (2011). Learning Valued Relations from Data. In: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., De Baets, B. (eds) Eurofuse 2011. Advances in Intelligent and Soft Computing, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24001-0_24

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  • DOI: https://doi.org/10.1007/978-3-642-24001-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24000-3

  • Online ISBN: 978-3-642-24001-0

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