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== Used References ==
 
== Used References ==
−
    1.
+
1. S.Agarwal, T.Graepel, R.Herbrich, S.Har-Peled, D.Roth, Generalization bounds for the area under the ROC curve. J. Mach. Learn. Res. 6, 393–425 (2005)MathSciNet
−
    S.Agarwal, T.Graepel, R.Herbrich, S.Har-Peled, D.Roth, Generalization bounds for the area under the ROC curve. J. Mach. Learn. Res. 6, 393–425 (2005)MathSciNet
+
      
−
     2.
+
2. A.Agresti, Categorical Data Analysis, 2nd version. (Wiley, 2002)
−
    A.Agresti, Categorical Data Analysis, 2nd version. (Wiley, 2002)
+
      
−
     3.
+
3.
 
     K.Ataman, N.Street, Y.Zhang, Learning to rank by maximizing AUC with linear programming, in Proceedings of the IEEE International Joint Conference on Neural Networks(Vancouver, BC, Canada, 2006), pp. 123–129
 
     K.Ataman, N.Street, Y.Zhang, Learning to rank by maximizing AUC with linear programming, in Proceedings of the IEEE International Joint Conference on Neural Networks(Vancouver, BC, Canada, 2006), pp. 123–129
−
     4.
+
      
 +
4.
 
     C.J.C. Burges, A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov. 2(2), 121–167 (1998)CrossRef
 
     C.J.C. Burges, A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov. 2(2), 121–167 (1998)CrossRef
−
     5.
+
      
 +
5.
 
     Z.Cao, T.Qin, T.Liu, M.Tsai, H.Li, Learning to rank: from pairwise approach to listwise approach, in Proceedings of the International Conference on Machine Learning(Corvallis, OR, USA, 2007), pp. 129–136
 
     Z.Cao, T.Qin, T.Liu, M.Tsai, H.Li, Learning to rank: from pairwise approach to listwise approach, in Proceedings of the International Conference on Machine Learning(Corvallis, OR, USA, 2007), pp. 129–136
−
     6.
+
      
 +
6.
 
     K.Cao-Van, Supervised Ranking, from semantics to algorithms. PhD thesis, Ghent University, Belgium, 2003
 
     K.Cao-Van, Supervised Ranking, from semantics to algorithms. PhD thesis, Ghent University, Belgium, 2003
−
    7.
+
 
 +
7.
 
     W.Chu, Z.Ghahramani, Gaussian processes for ordinal regression. J. Mach. Learn. Res. 6, 1019–1041 (2005)MathSciNetMATH
 
     W.Chu, Z.Ghahramani, Gaussian processes for ordinal regression. J. Mach. Learn. Res. 6, 1019–1041 (2005)MathSciNetMATH
−
     8.
+
      
 +
8.
 
     W.Chu, Z.Ghahramani, Preference learning with Gaussian processes, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 137–144
 
     W.Chu, Z.Ghahramani, Preference learning with Gaussian processes, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 137–144
−
     9.
+
      
 +
9.
 
     W.Chu, S.Keerthi, New approaches to support vector ordinal regression, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 321–328
 
     W.Chu, S.Keerthi, New approaches to support vector ordinal regression, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 321–328
−
     10.
+
      
 +
10.
 
     W.Chu, S.Keerthi, Support vector ordinal regression. Neural Comput. 19(3), 792–815 (2007)
 
     W.Chu, S.Keerthi, Support vector ordinal regression. Neural Comput. 19(3), 792–815 (2007)
−
     11.
+
      
 +
11.
 
     S.Clémençon, N.Vayatis, Ranking the best instances. J. Mach. Learn. Res. 8, 2671–2699 (2007)MathSciNetMATH
 
     S.Clémençon, N.Vayatis, Ranking the best instances. J. Mach. Learn. Res. 8, 2671–2699 (2007)MathSciNetMATH
−
     12.
+
      
 +
12.
 
     W.Cohen, R.Schapire, Y.Singer, Learning to order things, in Advances in Neural Information Processing Systems, vol.10 (MIT, Vancouver, Canada, 1998), pp. 451–457
 
     W.Cohen, R.Schapire, Y.Singer, Learning to order things, in Advances in Neural Information Processing Systems, vol.10 (MIT, Vancouver, Canada, 1998), pp. 451–457
−
     13.
+
      
 +
13.
 
     C.Cortes, M.Mohri, AUC optimization versus error rate minimization, in Advances in Neural Information Processing Systems, vol.16 (MIT, Vancouver, Canada, 2003), pp. 313–320
 
     C.Cortes, M.Mohri, AUC optimization versus error rate minimization, in Advances in Neural Information Processing Systems, vol.16 (MIT, Vancouver, Canada, 2003), pp. 313–320
−
     14.
+
      
 +
14.
 
     C.Cortes, M.Mohri. Confidence intervals for the area under the ROC curve, in Advances in Neural Information Processing Systems, vol.17 (MIT, Vancouver, Canada, 2004), pp. 305–312
 
     C.Cortes, M.Mohri. Confidence intervals for the area under the ROC curve, in Advances in Neural Information Processing Systems, vol.17 (MIT, Vancouver, Canada, 2004), pp. 305–312
−
     15.
+
      
 +
15.
 
     C.Cortes, M.Mohri, A.Rastogi, Magnitude-preserving ranking algorithms, in Proceedings of the International Conference on Machine Learning(Corvallis, OR, USA, 2007), pp. 169–176
 
     C.Cortes, M.Mohri, A.Rastogi, Magnitude-preserving ranking algorithms, in Proceedings of the International Conference on Machine Learning(Corvallis, OR, USA, 2007), pp. 169–176
−
     16.
+
      
 +
16.
 
     K.Crammer, Y.Singer, Pranking with ranking, in Proceedings of the Conference on Neural Information Processing Systems(Vancouver, Canada, 2001), pp. 641–647
 
     K.Crammer, Y.Singer, Pranking with ranking, in Proceedings of the Conference on Neural Information Processing Systems(Vancouver, Canada, 2001), pp. 641–647
−
     17.
+
      
 +
17.
 
     N.Cristianini, J.Shawe-Taylor, An Introduction to Support Vector Machines(Cambridge University Press, 2000)
 
     N.Cristianini, J.Shawe-Taylor, An Introduction to Support Vector Machines(Cambridge University Press, 2000)
−
     18.
+
      
 +
18.
 
     B.De Baets, H.De Meyer, Transitivity frameworks for reciprocal relations: cycle-transitivity versus { FG}-transitivity. Fuzzy Sets Syst. 152, 249–270 (2005)MATHCrossRef
 
     B.De Baets, H.De Meyer, Transitivity frameworks for reciprocal relations: cycle-transitivity versus { FG}-transitivity. Fuzzy Sets Syst. 152, 249–270 (2005)MATHCrossRef
−
     19.
+
      
 +
19.
 
     B.De Baets, H.De Meyer, B.De Schuymer, S.Jenei, Cyclic evaluation of transitivity of reciprocal relations. Soc. Choice Welfare 26, 217–238 (2006)MATHCrossRef
 
     B.De Baets, H.De Meyer, B.De Schuymer, S.Jenei, Cyclic evaluation of transitivity of reciprocal relations. Soc. Choice Welfare 26, 217–238 (2006)MATHCrossRef
−
     20.
+
      
 +
20.
 
     B.De Schuymer, H.De Meyer, B.De Baets, Cycle-transitive comparison of independent random variables. J. Multivar. Anal. 96, 352–373 (2005)MATHCrossRef
 
     B.De Schuymer, H.De Meyer, B.De Baets, Cycle-transitive comparison of independent random variables. J. Multivar. Anal. 96, 352–373 (2005)MATHCrossRef
−
     21.
+
      
 +
21.
 
     B.De Schuymer, H.De Meyer, B.De Baets, S.Jenei, On the cycle-transitivity of the dice model. Theory Decis. 54, 164–185 (2003)CrossRef
 
     B.De Schuymer, H.De Meyer, B.De Baets, S.Jenei, On the cycle-transitivity of the dice model. Theory Decis. 54, 164–185 (2003)CrossRef
−
     22.
+
      
 +
22.
 
     S.Dreiseitl, L.Ohno-Machado, M.Binder, Comparing three-class diagnostic tests by three-way ROC analysis. Med. Decis. Mak. 20, 323–331 (2000)CrossRef
 
     S.Dreiseitl, L.Ohno-Machado, M.Binder, Comparing three-class diagnostic tests by three-way ROC analysis. Med. Decis. Mak. 20, 323–331 (2000)CrossRef
−
     23.
+
      
 +
23.
 
     E.Frank, M.Hall, A simple approach to ordinal classification, in Proceedings of the European Conference on Machine Learning, (Freibourg, Germany, 2001), pp. 146–156
 
     E.Frank, M.Hall, A simple approach to ordinal classification, in Proceedings of the European Conference on Machine Learning, (Freibourg, Germany, 2001), pp. 146–156
−
     24.
+
      
 +
24.
 
     Y.Freund, R.Yier, R.Schapire, Y.Singer, An efficient boosting algorithm for combining preferences. J. Mach. Learn. Res. 4, 933–969 (2003)
 
     Y.Freund, R.Yier, R.Schapire, Y.Singer, An efficient boosting algorithm for combining preferences. J. Mach. Learn. Res. 4, 933–969 (2003)
−
     25.
+
      
 +
25.
 
     J.Fürnkranz, Round robin classification. J. Mach. Learn. Res. 2, 723–747 (2002)
 
     J.Fürnkranz, Round robin classification. J. Mach. Learn. Res. 2, 723–747 (2002)
−
     26.
+
      
 +
26.
 
     J.Fürnkranz, E.Hüllermeier, Pairwise preference learning and ranking. Lect. Notes Comput. Sci. 2837, 145–156 (2003)CrossRef
 
     J.Fürnkranz, E.Hüllermeier, Pairwise preference learning and ranking. Lect. Notes Comput. Sci. 2837, 145–156 (2003)CrossRef
−
     27.
+
      
 +
27.
 
     M.Gönen, G.Heller, Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92(4), 965–970 (2005)MathSciNetMATHCrossRef
 
     M.Gönen, G.Heller, Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92(4), 965–970 (2005)MathSciNetMATHCrossRef
−
     28.
+
      
 +
28.
 
     D.Hand, R.Till, A simple generalization of the area under the ROC curve for multiple class problems. Mach. Learn. 45, 171–186 (2001)MATHCrossRef
 
     D.Hand, R.Till, A simple generalization of the area under the ROC curve for multiple class problems. Mach. Learn. 45, 171–186 (2001)MATHCrossRef
−
     29.
+
      
 +
29.
 
     J.Hanley, B.McNeil, The meaning and use of the area under a receiver operating characteristics curve. Radiology 143, 29–36 (1982)
 
     J.Hanley, B.McNeil, The meaning and use of the area under a receiver operating characteristics curve. Radiology 143, 29–36 (1982)
−
     30.
+
      
 +
30.
 
     J.Hanley, B.McNeil, A method of comparing receiver operating characteristics curves derived from the same class. Radiology 148, 839–843 (1983)
 
     J.Hanley, B.McNeil, A method of comparing receiver operating characteristics curves derived from the same class. Radiology 148, 839–843 (1983)
−
     31.
+
      
 +
31.
 
     S.Har-Peled, D.Roth, D.Zimak, Constraint classification: A new approach to multi-class classification and ranking, in Advances in Neural Information Processing Systems, vol.15 (MIT, Vancouver, Canada, 2002), pp. 785–792
 
     S.Har-Peled, D.Roth, D.Zimak, Constraint classification: A new approach to multi-class classification and ranking, in Advances in Neural Information Processing Systems, vol.15 (MIT, Vancouver, Canada, 2002), pp. 785–792
−
     32.
+
      
 +
32.
 
     E.Harrington, Online ranking/collaborative filtering using the perceptron algorithm, in Proceedings of the 20th International Conference on Machine Learning(Washington, USA, 2003), pp. 250–257
 
     E.Harrington, Online ranking/collaborative filtering using the perceptron algorithm, in Proceedings of the 20th International Conference on Machine Learning(Washington, USA, 2003), pp. 250–257
−
     33.
+
      
 +
33.
 
     T.Hastie, R.Tibshirani, Classification by pairwise coupling. Ann. Stat. 26(2), 451–471 (1998)MathSciNetMATH
 
     T.Hastie, R.Tibshirani, Classification by pairwise coupling. Ann. Stat. 26(2), 451–471 (1998)MathSciNetMATH
−
     34.
+
      
 +
34.
 
     M.Heller, B.Schnörr, Learning sparse representations by non-negative matrix factorization and sequential cone programming. J. Mach. Learn. Res. 7, 1385–1407 (2006)MathSciNet
 
     M.Heller, B.Schnörr, Learning sparse representations by non-negative matrix factorization and sequential cone programming. J. Mach. Learn. Res. 7, 1385–1407 (2006)MathSciNet
−
     35.
+
      
 +
35.
 
     R.Herbrich, T.Graepel, K.Obermayer, Large margin rank boundaries for ordinal regression, in Advances in Large Margin Classifiers, ed. by A.Smola, P.Bartlett, B.Schölkopf, D.Schuurmans (MIT, 2000), pp. 115–132
 
     R.Herbrich, T.Graepel, K.Obermayer, Large margin rank boundaries for ordinal regression, in Advances in Large Margin Classifiers, ed. by A.Smola, P.Bartlett, B.Schölkopf, D.Schuurmans (MIT, 2000), pp. 115–132
−
     36.
+
      
 +
36.
 
     A.Herschtal, B.Raskutti, Optimizing area under the ROC curve using gradient descent, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 49–57
 
     A.Herschtal, B.Raskutti, Optimizing area under the ROC curve using gradient descent, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 49–57
−
     37.
+
      
 +
37.
 
     J.Higgins, Introduction to Modern Nonparametric Statistics(Duxbury, 2004)
 
     J.Higgins, Introduction to Modern Nonparametric Statistics(Duxbury, 2004)
−
     38.
+
      
 +
38.
 
     E.Hüllermeier, J.Hühn, Is an ordinal class structure useful in classifier learning? Int. J. Data Min. Model. Manag. 1(1), 45–67 (2009)
 
     E.Hüllermeier, J.Hühn, Is an ordinal class structure useful in classifier learning? Int. J. Data Min. Model. Manag. 1(1), 45–67 (2009)
−
     39.
+
      
 +
39.
 
     T.Joachims, A support vector method for multivariate performance measures, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 377–384
 
     T.Joachims, A support vector method for multivariate performance measures, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 377–384
−
     40.
+
      
 +
40.
 
     J.Kelley, The cutting plane method for convex programs. J. Soc. Ind. Appl. Math. 9, 703–712 (1960)MathSciNet
 
     J.Kelley, The cutting plane method for convex programs. J. Soc. Ind. Appl. Math. 9, 703–712 (1960)MathSciNet
−
     41.
+
      
 +
41.
 
     S.Kramer, G.Widmer, B.Pfahringer, M.Degroeve, Prediction of ordinal classes using regression trees. Fundam. Informaticae 24, 1–15 (2000)MathSciNet
 
     S.Kramer, G.Widmer, B.Pfahringer, M.Degroeve, Prediction of ordinal classes using regression trees. Fundam. Informaticae 24, 1–15 (2000)MathSciNet
−
     42.
+
      
 +
42.
 
     G.Lanckriet, N.Cristianini, P.Bartlett, L.El Gaoui, M.Jordan, Learning the kernel matrix with semidefinite programming. J. Mach. Learn. Res. 5, 27–72 (2004)MATH
 
     G.Lanckriet, N.Cristianini, P.Bartlett, L.El Gaoui, M.Jordan, Learning the kernel matrix with semidefinite programming. J. Mach. Learn. Res. 5, 27–72 (2004)MATH
−
     43.
+
      
 +
43.
 
     L.Lehmann, Nonparametrics: Statistical Methods based on Ranks(Holden Day, 1975)
 
     L.Lehmann, Nonparametrics: Statistical Methods based on Ranks(Holden Day, 1975)
−
     44.
+
      
 +
44.
 
     S.Lievens, B.De Baets, K.Cao-Van, A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting. Ann. Oper. Res. 163, 115–142 (2008)MathSciNetMATHCrossRef
 
     S.Lievens, B.De Baets, K.Cao-Van, A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting. Ann. Oper. Res. 163, 115–142 (2008)MathSciNetMATHCrossRef
−
     45.
+
      
 +
45.
 
     H.Lin, L.Li, Large-margin thresholded ensembles for ordinal regression: Theory and practice. Lect. Notes Comput. Sci. 4264, 319–333 (2006)CrossRef
 
     H.Lin, L.Li, Large-margin thresholded ensembles for ordinal regression: Theory and practice. Lect. Notes Comput. Sci. 4264, 319–333 (2006)CrossRef
−
     46.
+
      
 +
46.
 
     R.Luce, P.Suppes, Handbook of Mathematical Psychology, chapter Preference, Utility and Subjective Probability (Wiley, 1965), pp. 249–410
 
     R.Luce, P.Suppes, Handbook of Mathematical Psychology, chapter Preference, Utility and Subjective Probability (Wiley, 1965), pp. 249–410
−
     47.
+
      
 +
47.
 
     P.McCullagh, Regression models for ordinal data. J. R. Stat. Soc. B 42(2), 109–142 (1980)MathSciNetMATH
 
     P.McCullagh, Regression models for ordinal data. J. R. Stat. Soc. B 42(2), 109–142 (1980)MathSciNetMATH
−
     48.
+
      
 +
48.
 
     C.Nakas, C.Yiannoutsos, Ordered multiple-class ROC analysis with continuous measurements. Stat. Med. 22, 3437–3449 (2004)CrossRef
 
     C.Nakas, C.Yiannoutsos, Ordered multiple-class ROC analysis with continuous measurements. Stat. Med. 22, 3437–3449 (2004)CrossRef
−
     49.
+
      
 +
49.
 
     M.Öztürk, A.Tsoukiàs, Ph. Vincke, Preference modelling, in Multiple Criteria Decision Analysis. State of the Art Surveys, ed. by J.Figueira, S.Greco, M.Ehrgott (Springer, 2005), pp. 27–71
 
     M.Öztürk, A.Tsoukiàs, Ph. Vincke, Preference modelling, in Multiple Criteria Decision Analysis. State of the Art Surveys, ed. by J.Figueira, S.Greco, M.Ehrgott (Springer, 2005), pp. 27–71
−
     50.
+
      
 +
50.
 
     J.Platt, N.Cristianini, J.Shawe-Taylor, Large margin DAGs for multiclass classification. Adv. Neural Process. Syst. 12, 547–553 (2000)
 
     J.Platt, N.Cristianini, J.Shawe-Taylor, Large margin DAGs for multiclass classification. Adv. Neural Process. Syst. 12, 547–553 (2000)
−
     51.
+
      
 +
51.
 
     R.Potharst, J.C. Bioch, Decision trees for ordinal classification. Intell. Data Process. 4(2) (2000)
 
     R.Potharst, J.C. Bioch, Decision trees for ordinal classification. Intell. Data Process. 4(2) (2000)
−
     52.
+
      
 +
52.
 
     J.D. Rennie, N.Srebro, Loss functions for preference levels: Regression with discrete, ordered labels in Proceedings of the IJCAI Multidisciplinary Workshop on Advances in Preference Handling, (Edinburgh, Scotland, 2005), pp. 180–186
 
     J.D. Rennie, N.Srebro, Loss functions for preference levels: Regression with discrete, ordered labels in Proceedings of the IJCAI Multidisciplinary Workshop on Advances in Preference Handling, (Edinburgh, Scotland, 2005), pp. 180–186
−
     53.
+
      
 +
53.
 
     R.Rifkin, A.Klautau, In defense of one-versus-all classification. J. Mach. Learn. Res. 5, 101–143 (2004)MathSciNetMATH
 
     R.Rifkin, A.Klautau, In defense of one-versus-all classification. J. Mach. Learn. Res. 5, 101–143 (2004)MathSciNetMATH
−
     54.
+
      
 +
54.
 
     B.Schölkopf, A.Smola. Learning with Kernels, Support Vector Machines, Regularisation, Optimization and Beyond(MIT, 2002)
 
     B.Schölkopf, A.Smola. Learning with Kernels, Support Vector Machines, Regularisation, Optimization and Beyond(MIT, 2002)
−
     55.
+
      
 +
55.
 
     A.Shashua, A.Levin, Ranking with large margin principle: Two approaches, in Advances in Neural Information Processing Systems, vol.16 (MIT, Vancouver, Canada, 2003), pp. 937–944
 
     A.Shashua, A.Levin, Ranking with large margin principle: Two approaches, in Advances in Neural Information Processing Systems, vol.16 (MIT, Vancouver, Canada, 2003), pp. 937–944
−
     56.
+
      
 +
56.
 
     V.Torra, J.Domingo-Ferrer, J.M. Mateo-Sanz, M.Ng, Regression for ordinal variables without underlying continuous variables. Inf. Sci. 176, 465–476 (2006)MathSciNetCrossRef
 
     V.Torra, J.Domingo-Ferrer, J.M. Mateo-Sanz, M.Ng, Regression for ordinal variables without underlying continuous variables. Inf. Sci. 176, 465–476 (2006)MathSciNetCrossRef
−
     57.
+
      
 +
57.
 
     Y.Tsochantaridis, T.Joachims, T.Hofmann, Y.Altun, Large margin methods for structured and independent output variables. J. Mach. Learn. Res. 6, 1453–1484 (2005)MathSciNetMATH
 
     Y.Tsochantaridis, T.Joachims, T.Hofmann, Y.Altun, Large margin methods for structured and independent output variables. J. Mach. Learn. Res. 6, 1453–1484 (2005)MathSciNetMATH
−
     58.
+
      
 +
58.
 
     G.Tutz, K.Hechenbichler, Aggregating classifiers with ordinal response structure. J. Stat. Comput. Simul. 75(5), (2004)
 
     G.Tutz, K.Hechenbichler, Aggregating classifiers with ordinal response structure. J. Stat. Comput. Simul. 75(5), (2004)
−
     59.
+
      
 +
59.
 
     W.Waegeman, B.De Baets, On the ERA ranking representability of multi-class classifiers. Artif. Intell. (2009) submitted
 
     W.Waegeman, B.De Baets, On the ERA ranking representability of multi-class classifiers. Artif. Intell. (2009) submitted
−
     60.
+
      
 +
60.
 
     W.Waegeman, B.De Baets, L.Boullart, Learning a layered graph with a maximal number of paths connecting source and sink, in Proceedings of the ICML Workshop on Constrained Optimization and Structured Output Spaces(Corvallis, OR, USA, 2007)
 
     W.Waegeman, B.De Baets, L.Boullart, Learning a layered graph with a maximal number of paths connecting source and sink, in Proceedings of the ICML Workshop on Constrained Optimization and Structured Output Spaces(Corvallis, OR, USA, 2007)
−
     61.
+
      
 +
61.
 
     W.Waegeman, B.De Baets, L.Boullart, Learning layered ranking functions with structured support vector machines. Neural Netw. 21(10), 1511–1523 (2008)MATHCrossRef
 
     W.Waegeman, B.De Baets, L.Boullart, Learning layered ranking functions with structured support vector machines. Neural Netw. 21(10), 1511–1523 (2008)MATHCrossRef
−
     62.
+
      
 +
62.
 
     W.Waegeman, B.De Baets, L.Boullart, On the scalability of ordered multi-class ROC analysis. Comput. Stat. Data Anal. 52, 3371–3388 (2008)MATHCrossRef
 
     W.Waegeman, B.De Baets, L.Boullart, On the scalability of ordered multi-class ROC analysis. Comput. Stat. Data Anal. 52, 3371–3388 (2008)MATHCrossRef
−
     63.
+
      
 +
63.
 
     W.Waegeman, B.De Baets, L.Boullart, ROC analysis in ordinal regression learning. Pattern Recognit. Lett. 29, 1–9 (2008)CrossRef
 
     W.Waegeman, B.De Baets, L.Boullart, ROC analysis in ordinal regression learning. Pattern Recognit. Lett. 29, 1–9 (2008)CrossRef
−
     64.
+
      
 +
64.
 
     J.Xu, Y.Cao, H.Li, Y.Huang, Cost-sensitive learning of SVM for ranking, in Proceedings of the 17th European Conference on Machine Learning(Berlin, Germany, 2006), pp. 833–840
 
     J.Xu, Y.Cao, H.Li, Y.Huang, Cost-sensitive learning of SVM for ranking, in Proceedings of the 17th European Conference on Machine Learning(Berlin, Germany, 2006), pp. 833–840
−
     65.
+
      
 +
65.
 
     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), pp. 848–855
 
     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), pp. 848–855
−
     66.
+
      
 +
66.
 
     S.Yu, K.Yu, V.Tresp, H.Kriegel, Collaborative ordinal regression, in Proceedings of the International Conference on Machine Learning(Pittsburgh, PA, 2006), pp. 1089–1096
 
     S.Yu, K.Yu, V.Tresp, H.Kriegel, Collaborative ordinal regression, in Proceedings of the International Conference on Machine Learning(Pittsburgh, PA, 2006), pp. 1089–1096
  
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W. Waegeman: Learning  to  Rank:  a  ROC-based  Graph-Theoretic  Approach. 4OR quarterly journal of the Belgian, French and Italian Operations Research Societies 7(4): 399-402 · November 2009 http://link.springer.com/article/10.1007%2Fs10288-009-0095-y
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W. Waegeman. Learning to Rank: a ROC-based Graph-Theoretic Approach, Ghent University, October 2008 http://users.ugent.be/~wwaegemn/thesis.pdf

Version vom 29. November 2015, 14:12 Uhr

Reference

Willem Waegeman, Bernard De Baets: A Survey on ROC-based Ordinal Regression. In: Fürnkranz, J. and Hüllermeier, E.: Preference Learning, 2011, 127-154.

DOI

http://dx.doi.org/10.1007/978-3-642-14125-6_7

Abstract

Ordinal regression can be seen as a special case of preference learning, in which the class labels corresponding with data instances can take values from an ordered finite set. In such a setting, the classes usually have a linguistic interpretation attached by humans to subdivide the data into a number of preference bins. In this chapter, we give a general survey on ordinal regression from a machine learning point of view. In particular, we elaborate on some important connections with ROC analysis that have been introduced recently by the present authors. First, the important role of an underlying ranking function in ordinal regression models is discussed, as well as its impact on the performance evaluation of such models. Subsequently, we describe a new ROC-based performance measure that directly evaluates the underlying ranking function, and we place it in the more general context of ROC analysis as the volume under an r-dimensional ROC surface (VUS) for in general rclasses. Furthermore, we also discuss the scalability of this measure and show that it can be computed very efficiently for large samples. Finally, we present a kernel-based learning algorithm that optimizes VUS as a specific case of structured support vector machines.

Extended Abstract

Bibtex

@incollection{
year={2011},
isbn={978-3-642-14124-9},
booktitle={Preference Learning},
editor={Fürnkranz, Johannes and Hüllermeier, Eyke},
doi={10.1007/978-3-642-14125-6_7},
title={A Survey on ROC-based Ordinal Regression},
url={http://dx.doi.org/10.1007/978-3-642-14125-6_7, http://de.evo-art.org/index.php?title=A_Survey_on_ROC-based_Ordinal_Regression },
publisher={Springer Berlin Heidelberg},
author={Waegeman, Willem and Baets, BernardDe},
pages={127-154},
language={English}
}

Used References

1. S.Agarwal, T.Graepel, R.Herbrich, S.Har-Peled, D.Roth, Generalization bounds for the area under the ROC curve. J. Mach. Learn. Res. 6, 393–425 (2005)MathSciNet

2. A.Agresti, Categorical Data Analysis, 2nd version. (Wiley, 2002)

3. 

   K.Ataman, N.Street, Y.Zhang, Learning to rank by maximizing AUC with linear programming, in Proceedings of the IEEE International Joint Conference on Neural Networks(Vancouver, BC, Canada, 2006), pp. 123–129

4. 

   C.J.C. Burges, A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov. 2(2), 121–167 (1998)CrossRef

5. 

   Z.Cao, T.Qin, T.Liu, M.Tsai, H.Li, Learning to rank: from pairwise approach to listwise approach, in Proceedings of the International Conference on Machine Learning(Corvallis, OR, USA, 2007), pp. 129–136

6. 

   K.Cao-Van, Supervised Ranking, from semantics to algorithms. PhD thesis, Ghent University, Belgium, 2003

7. 

   W.Chu, Z.Ghahramani, Gaussian processes for ordinal regression. J. Mach. Learn. Res. 6, 1019–1041 (2005)MathSciNetMATH

8. 

   W.Chu, Z.Ghahramani, Preference learning with Gaussian processes, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 137–144

9. 

   W.Chu, S.Keerthi, New approaches to support vector ordinal regression, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 321–328

10. 

   W.Chu, S.Keerthi, Support vector ordinal regression. Neural Comput. 19(3), 792–815 (2007)

11. 

   S.Clémençon, N.Vayatis, Ranking the best instances. J. Mach. Learn. Res. 8, 2671–2699 (2007)MathSciNetMATH

12. 

   W.Cohen, R.Schapire, Y.Singer, Learning to order things, in Advances in Neural Information Processing Systems, vol.10 (MIT, Vancouver, Canada, 1998), pp. 451–457

13. 

   C.Cortes, M.Mohri, AUC optimization versus error rate minimization, in Advances in Neural Information Processing Systems, vol.16 (MIT, Vancouver, Canada, 2003), pp. 313–320

14. 

   C.Cortes, M.Mohri. Confidence intervals for the area under the ROC curve, in Advances in Neural Information Processing Systems, vol.17 (MIT, Vancouver, Canada, 2004), pp. 305–312

15. 

   C.Cortes, M.Mohri, A.Rastogi, Magnitude-preserving ranking algorithms, in Proceedings of the International Conference on Machine Learning(Corvallis, OR, USA, 2007), pp. 169–176

16. 

   K.Crammer, Y.Singer, Pranking with ranking, in Proceedings of the Conference on Neural Information Processing Systems(Vancouver, Canada, 2001), pp. 641–647

17. 

   N.Cristianini, J.Shawe-Taylor, An Introduction to Support Vector Machines(Cambridge University Press, 2000)

18. 

   B.De Baets, H.De Meyer, Transitivity frameworks for reciprocal relations: cycle-transitivity versus { FG}-transitivity. Fuzzy Sets Syst. 152, 249–270 (2005)MATHCrossRef

19. 

   B.De Baets, H.De Meyer, B.De Schuymer, S.Jenei, Cyclic evaluation of transitivity of reciprocal relations. Soc. Choice Welfare 26, 217–238 (2006)MATHCrossRef

20. 

   B.De Schuymer, H.De Meyer, B.De Baets, Cycle-transitive comparison of independent random variables. J. Multivar. Anal. 96, 352–373 (2005)MATHCrossRef

21. 

   B.De Schuymer, H.De Meyer, B.De Baets, S.Jenei, On the cycle-transitivity of the dice model. Theory Decis. 54, 164–185 (2003)CrossRef

22. 

   S.Dreiseitl, L.Ohno-Machado, M.Binder, Comparing three-class diagnostic tests by three-way ROC analysis. Med. Decis. Mak. 20, 323–331 (2000)CrossRef

23. 

   E.Frank, M.Hall, A simple approach to ordinal classification, in Proceedings of the European Conference on Machine Learning, (Freibourg, Germany, 2001), pp. 146–156

24. 

   Y.Freund, R.Yier, R.Schapire, Y.Singer, An efficient boosting algorithm for combining preferences. J. Mach. Learn. Res. 4, 933–969 (2003)

25. 

   J.Fürnkranz, Round robin classification. J. Mach. Learn. Res. 2, 723–747 (2002)

26. 

   J.Fürnkranz, E.Hüllermeier, Pairwise preference learning and ranking. Lect. Notes Comput. Sci. 2837, 145–156 (2003)CrossRef

27. 

   M.Gönen, G.Heller, Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92(4), 965–970 (2005)MathSciNetMATHCrossRef

28. 

   D.Hand, R.Till, A simple generalization of the area under the ROC curve for multiple class problems. Mach. Learn. 45, 171–186 (2001)MATHCrossRef

29. 

   J.Hanley, B.McNeil, The meaning and use of the area under a receiver operating characteristics curve. Radiology 143, 29–36 (1982)

30. 

   J.Hanley, B.McNeil, A method of comparing receiver operating characteristics curves derived from the same class. Radiology 148, 839–843 (1983)

31. 

   S.Har-Peled, D.Roth, D.Zimak, Constraint classification: A new approach to multi-class classification and ranking, in Advances in Neural Information Processing Systems, vol.15 (MIT, Vancouver, Canada, 2002), pp. 785–792

32. 

   E.Harrington, Online ranking/collaborative filtering using the perceptron algorithm, in Proceedings of the 20th International Conference on Machine Learning(Washington, USA, 2003), pp. 250–257

33. 

   T.Hastie, R.Tibshirani, Classification by pairwise coupling. Ann. Stat. 26(2), 451–471 (1998)MathSciNetMATH

34. 

   M.Heller, B.Schnörr, Learning sparse representations by non-negative matrix factorization and sequential cone programming. J. Mach. Learn. Res. 7, 1385–1407 (2006)MathSciNet

35. 

   R.Herbrich, T.Graepel, K.Obermayer, Large margin rank boundaries for ordinal regression, in Advances in Large Margin Classifiers, ed. by A.Smola, P.Bartlett, B.Schölkopf, D.Schuurmans (MIT, 2000), pp. 115–132

36. 

   A.Herschtal, B.Raskutti, Optimizing area under the ROC curve using gradient descent, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 49–57

37. 

   J.Higgins, Introduction to Modern Nonparametric Statistics(Duxbury, 2004)

38. 

   E.Hüllermeier, J.Hühn, Is an ordinal class structure useful in classifier learning? Int. J. Data Min. Model. Manag. 1(1), 45–67 (2009)

39. 

   T.Joachims, A support vector method for multivariate performance measures, in Proceedings of the International Conference on Machine Learning(Bonn, Germany, 2005), pp. 377–384

40. 

   J.Kelley, The cutting plane method for convex programs. J. Soc. Ind. Appl. Math. 9, 703–712 (1960)MathSciNet

41. 

   S.Kramer, G.Widmer, B.Pfahringer, M.Degroeve, Prediction of ordinal classes using regression trees. Fundam. Informaticae 24, 1–15 (2000)MathSciNet

42. 

   G.Lanckriet, N.Cristianini, P.Bartlett, L.El Gaoui, M.Jordan, Learning the kernel matrix with semidefinite programming. J. Mach. Learn. Res. 5, 27–72 (2004)MATH

43. 

   L.Lehmann, Nonparametrics: Statistical Methods based on Ranks(Holden Day, 1975)

44. 

   S.Lievens, B.De Baets, K.Cao-Van, A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting. Ann. Oper. Res. 163, 115–142 (2008)MathSciNetMATHCrossRef

45. 

   H.Lin, L.Li, Large-margin thresholded ensembles for ordinal regression: Theory and practice. Lect. Notes Comput. Sci. 4264, 319–333 (2006)CrossRef

46. 

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

47. 

   P.McCullagh, Regression models for ordinal data. J. R. Stat. Soc. B 42(2), 109–142 (1980)MathSciNetMATH

48. 

   C.Nakas, C.Yiannoutsos, Ordered multiple-class ROC analysis with continuous measurements. Stat. Med. 22, 3437–3449 (2004)CrossRef

49. 

   M.Öztürk, A.Tsoukiàs, Ph. Vincke, Preference modelling, in Multiple Criteria Decision Analysis. State of the Art Surveys, ed. by J.Figueira, S.Greco, M.Ehrgott (Springer, 2005), pp. 27–71

50. 

   J.Platt, N.Cristianini, J.Shawe-Taylor, Large margin DAGs for multiclass classification. Adv. Neural Process. Syst. 12, 547–553 (2000)

51. 

   R.Potharst, J.C. Bioch, Decision trees for ordinal classification. Intell. Data Process. 4(2) (2000)

52. 

   J.D. Rennie, N.Srebro, Loss functions for preference levels: Regression with discrete, ordered labels in Proceedings of the IJCAI Multidisciplinary Workshop on Advances in Preference Handling, (Edinburgh, Scotland, 2005), pp. 180–186

53. 

   R.Rifkin, A.Klautau, In defense of one-versus-all classification. J. Mach. Learn. Res. 5, 101–143 (2004)MathSciNetMATH

54. 

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

55. 

   A.Shashua, A.Levin, Ranking with large margin principle: Two approaches, in Advances in Neural Information Processing Systems, vol.16 (MIT, Vancouver, Canada, 2003), pp. 937–944

56. 

   V.Torra, J.Domingo-Ferrer, J.M. Mateo-Sanz, M.Ng, Regression for ordinal variables without underlying continuous variables. Inf. Sci. 176, 465–476 (2006)MathSciNetCrossRef

57. 

   Y.Tsochantaridis, T.Joachims, T.Hofmann, Y.Altun, Large margin methods for structured and independent output variables. J. Mach. Learn. Res. 6, 1453–1484 (2005)MathSciNetMATH

58. 

   G.Tutz, K.Hechenbichler, Aggregating classifiers with ordinal response structure. J. Stat. Comput. Simul. 75(5), (2004)

59. 

   W.Waegeman, B.De Baets, On the ERA ranking representability of multi-class classifiers. Artif. Intell. (2009) submitted

60. 

   W.Waegeman, B.De Baets, L.Boullart, Learning a layered graph with a maximal number of paths connecting source and sink, in Proceedings of the ICML Workshop on Constrained Optimization and Structured Output Spaces(Corvallis, OR, USA, 2007)

61. 

   W.Waegeman, B.De Baets, L.Boullart, Learning layered ranking functions with structured support vector machines. Neural Netw. 21(10), 1511–1523 (2008)MATHCrossRef

62. 

   W.Waegeman, B.De Baets, L.Boullart, On the scalability of ordered multi-class ROC analysis. Comput. Stat. Data Anal. 52, 3371–3388 (2008)MATHCrossRef

63. 

   W.Waegeman, B.De Baets, L.Boullart, ROC analysis in ordinal regression learning. Pattern Recognit. Lett. 29, 1–9 (2008)CrossRef

64. 

   J.Xu, Y.Cao, H.Li, Y.Huang, Cost-sensitive learning of SVM for ranking, in Proceedings of the 17th European Conference on Machine Learning(Berlin, Germany, 2006), pp. 833–840

65. 

   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), pp. 848–855

66. 

   S.Yu, K.Yu, V.Tresp, H.Kriegel, Collaborative ordinal regression, in Proceedings of the International Conference on Machine Learning(Pittsburgh, PA, 2006), pp. 1089–1096


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W. Waegeman: Learning to Rank: a ROC-based Graph-Theoretic Approach. 4OR quarterly journal of the Belgian, French and Italian Operations Research Societies 7(4): 399-402 · November 2009 http://link.springer.com/article/10.1007%2Fs10288-009-0095-y

W. Waegeman. Learning to Rank: a ROC-based Graph-Theoretic Approach, Ghent University, October 2008 http://users.ugent.be/~wwaegemn/thesis.pdf

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