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ERA ranking representability: the missing link between ordinal regression and multi-class classification

Willem Waegeman (UGent) and Bernard De Baets (UGent)
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Bioinformatics: from nucleotids to networks (N2N)
Abstract
Can a multi-class classification model in some situations be simplified to an ordinal regression model without sacrificing performance? We try to answer this question from a theoretical point of view for one-versus-one multi-class ensembles. To that end, sufficient conditions are derived for which a one-versus-one ensemble becomes ranking representable, i.e. conditions for which the ensemble can be reduced to a ranking or ordinal regression model such that a similar performance on training data is measured. As performance measure, we use the area under the ROC curve (AUC) and its reformulation in terms of graphs. For the three-class case, this results in a new type of cycle transitivity for pairwise AUCs that can be verified by solving an integer quadratic program. Moreover, solving this integer quadratic program can be avoided, since its solution converges for an infinite data sample to a simple form, resulting in a deviation bound that becomes tighter with increasing sample size.
Keywords
graph theory, integer programming, pattern classification, quadratic programming, regression analysis

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Chicago
Waegeman, Willem, and Bernard De Baets. 2011. “ERA Ranking Representability: The Missing Link Between Ordinal Regression and Multi-class Classification.” In Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA), 1188–1193. Piscataway, NJ, USA: IEEE.
APA
Waegeman, W., & De Baets, B. (2011). ERA ranking representability: the missing link between ordinal regression and multi-class classification. Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA) (pp. 1188–1193). Presented at the 11th International conference on Intelligent Systems Design and Applications (ISDA 2011), Piscataway, NJ, USA: IEEE.
Vancouver
1.
Waegeman W, De Baets B. ERA ranking representability: the missing link between ordinal regression and multi-class classification. Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA). Piscataway, NJ, USA: IEEE; 2011. p. 1188–93.
MLA
Waegeman, Willem, and Bernard De Baets. “ERA Ranking Representability: The Missing Link Between Ordinal Regression and Multi-class Classification.” Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA). Piscataway, NJ, USA: IEEE, 2011. 1188–1193. Print.
@inproceedings{2037292,
  abstract     = {Can a multi-class classification model in some situations be simplified to an ordinal regression model without sacrificing performance? We try to answer this question from a theoretical point of view for one-versus-one multi-class ensembles. To that end, sufficient conditions are derived for which a one-versus-one ensemble becomes ranking representable, i.e. conditions for which the ensemble can be reduced to a ranking or ordinal regression model such that a similar performance on training data is measured. As performance measure, we use the area under the ROC curve (AUC) and its reformulation in terms of graphs. For the three-class case, this results in a new type of cycle transitivity for pairwise AUCs that can be verified by solving an integer quadratic program. Moreover, solving this integer quadratic program can be avoided, since its solution converges for an infinite data sample to a simple form, resulting in a deviation bound that becomes tighter with increasing sample size.},
  author       = {Waegeman, Willem and De Baets, Bernard},
  booktitle    = {Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA)},
  isbn         = {9781457716768},
  keyword      = {graph theory,integer programming,pattern classification,quadratic programming,regression analysis},
  language     = {eng},
  location     = {Cordoba, Spain},
  pages        = {1188--1193},
  publisher    = {IEEE},
  title        = {ERA ranking representability: the missing link between ordinal regression and multi-class classification},
  url          = {http://dx.doi.org/10.1109/ISDA.2011.6121820},
  year         = {2011},
}

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