Adapting Decision DAGs for Multipartite Ranking

  • José Ramón Quevedo
  • Elena Montañés
  • Oscar Luaces
  • Juan José del Coz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6323)


Multipartite ranking is a special kind of ranking for problems in which classes exhibit an order. Many applications require its use, for instance, granting loans in a bank, reviewing papers in a conference or just grading exercises in an education environment. Several methods have been proposed for this purpose. The simplest ones resort to regression schemes with a pre- and post-process of the classes, what makes them barely useful. Other alternatives make use of class order information or they perform a pairwise classification together with an aggregation function. In this paper we present and discuss two methods based on building a Decision Directed Acyclic Graph (DDAG). Their performance is evaluated over a set of ordinal benchmark data sets according to the C-Index measure. Both yield competitive results with regard to state-of-the-art methods, specially the one based on a probabilistic approach, called PR-DDAG.


Base Learner Ordinal Regression Competent Model Global Ranking Machine Learn Research 
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.


  1. 1.
    Brinker, K., Hüllermeier, E.: Case-based label ranking. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 566–573. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Cardoso, J.S., da Costa, J.F.P.: Learning to classify ordinal data: The data replication method. Journal of Machine Learning Research 8, 1393–1429 (2007)Google Scholar
  3. 3.
    Chen, P., Liu, S.: An improved dag-svm for multi-class classification. International Conference on Natural Computation 1, 460–462 (2009)CrossRefGoogle Scholar
  4. 4.
    Chu, W., Sathiya Keerthi, S.: New approaches to support vector ordinal regression. In: De Raedt, L., Wrobel, S. (eds.) Proceedings of the ICML’05, vol. 119, pp. 145–152. ACM, New York (2005)Google Scholar
  5. 5.
    Demšar, J.: Statistical comparisons of classifiers over multiple data sets. Journal of Machine Learning Research 7, 1–30 (2006)Google Scholar
  6. 6.
    Fawcett, T.: An introduction to roc analysis. Pattern Recognition Letters 27(8), 861–874 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Feng, J., Yang, Y., Fan, J.: Fuzzy multi-class svm classifier based on optimal directed acyclic graph using in similar handwritten chinese characters recognition. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 875–880. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Frank, E., Hall, M.: A simple approach to ordinal classification. In: EMCL ’01: Proceedings of the 12th European Conference on Machine Learning, London, UK, pp. 145–156. Springer, Heidelberg (2001)Google Scholar
  9. 9.
    Friedman, J.H.: Another approach to polychotomous classification. Technical report, Department of Statistics, Stanford University (1996)Google Scholar
  10. 10.
    Fürnkranz, J.: Round robin classification. Journal of Machine Learning Research 2, 721–747 (2002)zbMATHCrossRefGoogle Scholar
  11. 11.
    Fürnkranz, J., Hüllermeier, E., Vanderlooy, S.: Binary decomposition methods for multipartite ranking. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds.) ECML PKDD 2009. LNCS, vol. 5781, pp. 359–374. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Gonen, M., Heller, G.: Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92(4), 965–970 (2005)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Hand, D.J., Till, R.J.: A simple generalisation of the area under the roc curve for multiple class classification problems. Machine Learning 45(2), 171–186 (2001)zbMATHCrossRefGoogle Scholar
  14. 14.
    Herbrich, R., Graepel, T., Obermayer, K.: Large margin rank boundaries for ordinal regression. In: Smola, Bartlett, Schoelkopf, Schuurmans (eds.) Advances in Large Margin Classifiers. MIT Press, Cambridge (2000)Google Scholar
  15. 15.
    Higgins, J.: Introduction to Modern Nonparametric Statistics. Duxbury Press, Boston (2004)Google Scholar
  16. 16.
    Hühn, J.C., Hüllermeier, E.: Is an ordinal class structure useful in classifier learning? Int. J. of Data Mining Modelling and Management 1(1), 45–67 (2008)zbMATHCrossRefGoogle Scholar
  17. 17.
    Hüllermeier, E., Fürnkranz, J., Cheng, W., Brinker, K.: Label ranking by learning pairwise preferences. Artificial Intelligence 172(16-17), 1897–1916 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Joachims, T.: A support vector method for multivariate performance measures. In: ICML ’05: Proceedings of the 22nd International Conference on Machine Learning, pp. 377–384. ACM, New York (2005)CrossRefGoogle Scholar
  19. 19.
    Kramer, S., Widmer, G., Pfahringer, B., de Groeve, M.: Prediction of ordinal classes using regression trees. In: Ohsuga, S., Raś, Z.W. (eds.) ISMIS 2000. LNCS (LNAI), vol. 1932, pp. 426–434. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  20. 20.
    Li, P., Burges, C.J.C., Wu, Q.: Mcrank: Learning to rank using multiple classification and gradient boosting. In: Platt, J.C., Koller, D., Singer, Y., Roweis, S.T. (eds.) NIPS. MIT Press, Cambridge (2007)Google Scholar
  21. 21.
    Lin, C.-J., Weng, R.C., Sathiya Keerthi, S.: Trust region newton method for logistic regression. Journal of Machine Learning Research 9, 627–650 (2008)Google Scholar
  22. 22.
    Luaces, O., Taboada, F., Albaiceta, G.M., Domínguez, L.A., Enríquez, P., Bahamonde, A.: Predicting the probability of survival in intensive care unit patients from a small number of variables and training examples. Artificial Intelligence in Medicine 45(1), 63–76 (2009)CrossRefGoogle Scholar
  23. 23.
    Nguyen, C.D., Dung, T.A., Cao, T.H.: Text classification for dag-structured categories. In: Ho, T.-B., Cheung, D., Liu, H. (eds.) PAKDD 2005. LNCS (LNAI), vol. 3518, pp. 290–300. Springer, Heidelberg (2005)Google Scholar
  24. 24.
    Platt, J.C., Cristianini, N., Shawe-taylor, J.: Large margin dags for multiclass classification. In: Advances in Neural Information Processing Systems, pp. 547–553. MIT Press, Cambridge (2000)Google Scholar
  25. 25.
    Platt, J.C., Platt, J.C.: Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In: Advances in Large Margin Classifiers, pp. 61–74. MIT Press, Cambridge (1999)Google Scholar
  26. 26.
    Rajaram, S., Agarwal, S.: Generalization bounds for k-partite ranking. In: Agarwal, S., Cortes, C., Herbrich, R. (eds.) Proceedings of the NIPS 2005 Workshop on Learning to Rank, pp. 28–23 (2005)Google Scholar
  27. 27.
    Takahashi, F., Abe, S.: Optimizing directed acyclic graph support vector machines. In: IAPR - TC3 International Workshop on Artificial Neural Networks in Pattern Recognition University of Florence, Italy (2003)Google Scholar
  28. 28.
    Vapnik, V., Chapelle, O.: Bounds on error expectation for support vector machines. Neural Computation 12(9), 2013–2036 (2000)CrossRefGoogle Scholar
  29. 29.
    Waegeman, W., De Baets, B., Boullart, L.: Roc analysis in ordinal regression learning. Pattern Recognition Letters 29(1), 1–9 (2008)CrossRefGoogle Scholar
  30. 30.
    Weiss, M.A.: Data structures and algorithm analysis in C, 2nd edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1997)Google Scholar
  31. 31.
    Wu, T.F., Lin, C.J., Weng, R.C.: Probability estimates for multi-class classification by pairwise coupling. J. of Machine Learning Research 5, 975–1005 (2004)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • José Ramón Quevedo
    • 1
  • Elena Montañés
    • 1
  • Oscar Luaces
    • 1
  • Juan José del Coz
    • 1
  1. 1.Artificial Intelligence CenterUniversity of Oviedo at GijónSpain

Personalised recommendations