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
Bowling, M., Fürnkranz, J., Graepel, T., Musick, R.: Machine learning and games. Machine learning 63(3), 211–215 (2006)
Yamanishi, Y., Vert, J.-P., Kanehisa, M.: Protein network inference from multiple genomic data: a supervised approach. Bioinformatics 20, 1363–1370 (2004)
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)
Taskar, B., Wong, M., Abbeel, P., Koller, D.: Link prediction in relational data. In: Advances in Neural Information Processing Systems (2004)
De Raedt, L.: Logical and Relational Learning. Springer, Heidelberg (2009)
Vert, J.-P., Yamanishi, Y.: Supervised graph inference. In: Advances in Neural Information Processing Systems, vol. 17 (2005)
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)
Hüllermeier, E., Fürnkranz, J.: Preference Learning. Springer, Heidelberg (2010)
Geurts, P., Touleimat, N., Dutreix, M., d’Alché-Buc, F.: Inferring biological networks with output kernel trees. BMC Bioinformatics 8(2), S4 (2007)
Doignon, J.-P., Monjardet, B., Roubens, M., Vincke, P.: Biorder families, valued relations and preference modelling. Journal of Mathematical Psychology 3030, 435–480 (1986)
Switalski, Z.: Transitivity of fuzzy preference relations - an empirical study. Fuzzy Sets and Systems 118, 503–508 (2000)
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)
Schölkopf, B., Smola, A.: Learning with Kernels, Support Vector Machines, Regularisation, Optimization and Beyond. The MIT Press, Cambridge (2002)
Ben-Hur, A., Noble, W.: Kernel methods for predicting protein-protein interactions. Bioinformatics 21(1), 38–46 (2005)
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)
Fisher, L.: Rock, Paper, Scissors: Game Theory in Everyday Life. Basic Books, New York (2008)
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)
Czárán, T., Hoekstra, R., Pagie, L.: Chemical warfare between microbes promotes biodiversity. Proceedings of the National Academy of Sciences 99(2), 786–790 (2002)
Nowak, M.: Biodiversity: Bacterial game dynamics. Nature 418, 138–139 (2002)
Kirkup, B., Riley, M.: Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428, 412–414 (2004)
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)
Reichenbach, T., Mobilia, M., Frey, E.: Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448, 1046–1049 (2007)
Boddy, L.: Interspecific combative interactions between wood-decaying basidiomycetes. FEMS Microbiology Ecology 31, 185–194 (2000)
Sinervo, S., Lively, C.: The rock-paper-scissors game and the evolution of alternative male strategies. Nature 340, 240–246 (1996)
Waite, T.: Intransitive preferences in hoarding gray jays (Perisoreus canadensis). Journal of Behavioural Ecology and Sociobiology 50, 116–121 (2001)
Luce, R., Suppes, P.: Preference, Utility and Subjective Probability. In: Handbook of Mathematical Psychology, pp. 249–410. Wiley, Chichester (1965)
Fishburn, P.: Nontransitive preferences in decision theory. Journal of Risk and Uncertainty 44, 113–134 (1991)
Tversky, A.: In: Shafir, E. (ed.) Preference, Belief and Similarity. MIT Press, Cambridge (1998)
Gower, J., Legendre, P.: Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification 3, 5–48 (1986)
Jäkel, F., Schölkopf, B., Wichmann, F.: Similarity, kernels, and the triangle inequality. Journal of Mathematical Psychology 52(2), 297–303 (2008)
Switalski, Z.: General transitivity conditions for fuzzy reciprocal preference matrices. Fuzzy Sets and Systems 137, 85–100 (2003)
De Baets, B., De Meyer, H.: Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity. Fuzzy Sets and Systems 152, 249–270 (2005)
De Baets, B., Mesiar, R.: Metrics and T-equalities. Journal of Mathematical Analysis and Applications 267, 531–547 (2002)
Moser, B.: On representing and generating kernels by fuzzy equivalence relations. Journal of Machine Learning Research 7, 2603–2620 (2006)
Billot, A.: An existence theorem for fuzzy utility functions: A new elementary proof. Fuzzy Sets and Systems 74, 271–276 (1995)
Koppen, M.: Random Utility Representation of Binary Choice Probilities: Critical Graphs yielding Critical Necessary Conditions. Journal of Mathematical Psychology 39, 21–39 (1995)
Fono, L., Andjiga, N.: Utility function of fuzzy preferences on a countable set under max-*-transitivity. Social Choice and Welfare 28, 667–683 (2007)
Bodenhofer, U., De Baets, B., Fodor, J.: A compendium of fuzzy weak orders. Fuzzy Sets and Systems 158, 811–829 (2007)
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)
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)
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)
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)
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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
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