Biorder families, valued relations and preference modelling
Journal of Mathematical Psychology
Convergence of powers of reciprocal fuzzy matrices
Information Sciences: an International Journal
An existence theorem for fuzzy utility functions: a new elementary proof
Fuzzy Sets and Systems
Journal of Mathematical Psychology
Topological sorting of large networks
Communications of the ACM
Robust Classification for Imprecise Environments
Machine Learning
On the existence and construction of T-transitive closures
Information Sciences: an International Journal
General transitivity conditions for fuzzy reciprocal preference matrices
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
The Journal of Machine Learning Research
Probability Estimates for Multi-class Classification by Pairwise Coupling
The Journal of Machine Learning Research
Generalization Bounds for the Area Under the ROC Curve
The Journal of Machine Learning Research
Cycle-transitive comparison of independent random variables
Journal of Multivariate Analysis
An introduction to ROC analysis
Pattern Recognition Letters - Special issue: ROC analysis in pattern recognition
On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis
Support Vector Ordinal Regression
Neural Computation
ROC analysis in ordinal regression learning
Pattern Recognition Letters
Consistent models of transitivity for reciprocal preferences on a finite ordinal scale
Information Sciences: an International Journal
Binary Decomposition Methods for Multipartite Ranking
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity
Fuzzy Sets and Systems
Regression for ordinal variables without underlying continuous variables
Information Sciences: an International Journal
On the cycle-transitivity of the mutual rank probability relation of a poset
Fuzzy Sets and Systems
On the cycle-transitivity of the mutual rank probability relation of a poset
Fuzzy Sets and Systems
On the ERA ranking representability of pairwise bipartite ranking functions
Artificial Intelligence
Information Sciences: an International Journal
Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
A vector-valued support vector machine model for multiclass problem
Information Sciences: an International Journal
On a certain class of aggregative operators
Information Sciences: an International Journal
Hi-index | 0.07 |
Many multi-class classification algorithms in statistics and machine learning typically combine several binary classifiers in order to construct an overall classifier. In the popular pairwise ensemble, one classifier is built for each pair of classes, resulting in pairwise bipartite rankings. In contrast, ordinal regression algorithms consider a single ranking function for several ordered classes. It is known in the literature that pairwise ensembles can be useful for ordinal regression. However, can single ranking models make a contribution to multi-class classification? The answer to this question should be affirmative, as supported by theoretical results presented in this article. We conduct a formal analysis of the consistency of pairwise bipartite rankings by uncovering the conditions under which they can be equivalently expressed in terms of a single ranking. Similar to the utility representability of pairwise preference relations, it turns out that transitivity plays a crucial role in the characterization of the ranking representability of pairwise bipartite rankings. To this end, we introduce the new concepts of strict ranking representability, a restrictive condition that can be verified easily, and AUC ranking representability, a practically more useful condition that is more difficult to verify. However, the link between pairwise bipartite rankings and dice games allows us to formulate necessary transitivity conditions for AUC ranking representability. A sufficient condition on the other hand is obtained by introducing a new type of transitivity that can be verified by solving an integer quadratic program.