A transitivity analysis of bipartite rankings in pairwise multi-class classification

Information Sciences

Volumn 180, Issue 21, 2010, Pages 4099-4117

  Waegeman, Willem ^a   De Baets, Bernard ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Bipartite ranking; Decision theory; Graph theory; Multi class classification; Ordinal regression; Reciprocal relation; ROC analysis; Transitivity

Indexed keywords

BIPARTITE RANKING; MULTI-CLASS CLASSIFICATION; ORDINAL REGRESSION; RECIPROCAL RELATIONS; ROC ANALYSIS; TRANSITIVITY;

CLASSIFIERS; GRAPH THEORY; INTEGER PROGRAMMING; REGRESSION ANALYSIS;

DECISION THEORY;

EID: 77958479631     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.06.036     Document Type: Article

References (46)

1. S. Agarwal, T. Graepel, R. Herbrich, S. Har-Peled, and D. Roth Generalization bounds for the area under the ROC curve Journal of Machine Learning Research 6 2005 393 425
2. A. Billot An existence theorem for fuzzy utility functions: a new elementary proof Fuzzy Sets and Systems 74 1995 271 276
3. W. Chu, and S. Keerthi Support vector ordinal regression Neural Computation 19 3 2007 792 815
4. C. Cortes, and M. Mohri AUC Optimization Versus Error Rate Minimization Advances in Neural Information Processing Systems vol. 16 2003 MIT Press Vancouver, Canada
5. M. Dasgupta, and R. Deb Transitivity and fuzzy preferences Social Choice and Welfare 13 1996 305 318
6. B. De Baets, and H. De Meyer On the existence and construction of T-transitive closures Information Sciences 152 2003 167 192
7. B. De Baets, and H. De Meyer Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity Fuzzy Sets and Systems 152 2005 249 270
8. B. De Baets, H. De Meyer, K. De Loof, On the cycle transitivity of the mutual rank probability relation of a poset, Fuzzy Sets and Systems, doi:10.1016/j.fss.2010.05.005.
9. B. De Baets, H. De Meyer, B. De Schuymer, and S. Jenei Cyclic evaluation of transitivity of reciprocal relations Social Choice and Welfare 26 2006 217 238
10. H. De Meyer, B. De Baets, and B. De Schuymer On the transitivity of the comonotonic and countermonotonic comparison of random variables Journal of Multivariate Analysis 98 2007 177 193
11. B. De Schuymer, H. De Meyer, and B. De Baets Cycle-transitive comparison of independent random variables Journal of Multivariate Analysis 96 2005 352 373
12. B. De Schuymer, H. De Meyer, and B. De Baets Extreme copulas and the comparison of ordered lists Theory and Decision 62 2007 195 217
13. B. De Schuymer, H. De Meyer, B. De Baets, and S. Jenei On the cycle-transitivity of the dice model Theory and Decision 54 2003 261 285
14. A. Di Nola, W. Kolodziejczyk, and S. Sessa Convergence of powers of fuzzy reciprocal matrices Information Sciences 75 1995 99 107
15. S. Diaz, J. García-Lapresta, and S. Montes Consistent models of transitivity for reciprocal preferences on a finite ordinal scale Information Sciences 178 13 2008 2832 2848
16. J. Doignon, B. Monjardet, M. Roubens, P. Vincke, and Biorder families valued relations and preference modelling Journal of Mathematical Psychology 30 1986 435 480
17. T. Fawcett An introduction to ROC analysis Pattern Recognition Letters 27 8 2006 861 874
18. C. Ferri, J. Hernandez-Orallo, M. Salido, Volume under ROC surface for multi-class problems, in: Proceedings of the European Conference on Machine Learning, Dubrovnik, Croatia, 2003.
19. J. Fieldsend, M. Everson, Formulation and comparison of multi-class ROC surfaces, in: Proceedings of the ICML Workshop on ROC Analysis in Machine Learning, Bonn, Germany, 2005.
20. P. Fishburn Utility Theory for Decision Making 1970 Wiley
21. P. Flach, The geometry of ROC space: understanding machine learning metrics through ROC isometrics, in: Proceedings of the International Conference on Machine Learning, Washington, DC, USA, 2003.
22. P. Flach, The many faces of ROC analysis in machine learning, Tutorial Presented at the European Conference on Machine Learning, Valencia, Spain, August 2004.
23. L. Fono, and N. Andjiga Utility function of fuzzy preferences on a countable set under max - transitivity Social Choice and Welfare 28 2007 667 683
24. J. Fürnkranz Round robin classification Journal of Machine Learning Research 2 2002 723 747
25. J. Fürnkranz, E. Hüllermeier, and S. Vanderlooy Binary decomposition methods for multipartite ranking Lecture Notes in Computer Science 5781 2009 359 374
26. D. Hand, and R. Till A simple generalization of the area under the ROC curve for multiple class problems Machine Learning 45 2001 171 186
27. J. Hanley, and B. McNeil The meaning and use of the area under a receiver operating characteristics curve Radiology 143 1982 29 36
28. T. Hastie, and R. Tibshirani Classification by pairwise coupling The Annals of Statistics 26 2 1998 451 471
29. R. Herbrich, T. Graepel, and K. Obermayer Large margin rank boundaries for ordinal regression A. Smola, P. Bartlett, B. Schölkopf, D. Schuurmans, Advances in Large Margin Classifiers 2000 MIT Press
30. E. Hüllermeier, J. Fürnkranz, Pairwise preference learning and ranking, in: Proceedings of the European Conference on Machine Learning, Dubrovnik, Croatia, 2003.
31. E. Hüllermeier, and J. Hühn Is an ordinal class structure useful in classifier learning? International Journal of Data Mining, Modelling and Management 1 1 2009 45 67
32. E. Hüllermeier, and S. Vanderlooy Combining predictions in pairwise classification: an optimal adaptive voting strategy and its relation to weighted voting Pattern Recognition 43 2010 129 142
33. A. Kahn Topological sorting of large networks Communications of the ACM 5 1962 558 562
34. M. Koppen Random utility representation of binary choice probabilities: critical graphs yielding critical necessary conditions Journal of Mathematical Psychology 39 1995 21 39
35. M. Krzysko, and W. Wolynski New variants of pairwise classification European Journal of Operational Research 199 2009 512 519
36. R. Luce, and P. Suppes Handbook of Mathematical Psychology Chapter. Preference, Utility and Subjective Probability 1965 Wiley
37. M. Öztürk, A. Tsoukis, and P. Vincke Preference modelling J. Figueira, S. Greco, M. Ehrgott, Multiple Criteria Decision Analysis. State of the Art Surveys 2005 Springer-Verlag 27 71
38. F. Provost, and T. Fawcett Robust classification for imprecise environments Machine Learning 42 2001 203 231
39. A. Schrijver Combinatorial Optimization 2003 Springer
40. Z. Switalski General transitivity conditions for fuzzy reciprocal preference matrices Fuzzy Sets and Systems 137 2003 85 100
41. V. Torra, J. Domingo-Ferrer, J. Mateo-Sanz, and M. Ng Regression for ordinal variables without underlying continuous variables Information Sciences 176 2006 465 476
42. A. Tversky Preference, Belief and Similarity 1998 MIT Press
43. W. Waegeman, B. De Baets, and L. Boullart Learning layered ranking functions with structured support vector machines Neural Networks 21 10 2008 1511 1523
44. W. Waegeman, B. De Baets, and L. Boullart ROC analysis in ordinal regression learning Pattern Recognition Letters 29 2008 1 9
45. F. Wu, C. Lin, and R. Weng Probability estimates for multi-class support vector machines by pairwise coupling Journal of Machine Learning Research 5 2004 975 1005
46. L. Yan, R. Dodier, M. Mozer, R. Wolniewiecz, Optimizing classifier performance via an approximation to the Wilcoxon-Mann-Whitney statistic, in: Proceedings of the International Conference on Machine Learning, Washington, DC, USA, 2003.