A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
An efficient boosting algorithm for combining preferences
The Journal of Machine Learning Research
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Optimising area under the ROC curve using gradient descent
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Generalization Bounds for the Area Under the ROC Curve
The Journal of Machine Learning Research
Large Margin Methods for Structured and Interdependent Output Variables
The Journal of Machine Learning Research
A support vector method for multivariate performance measures
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning from labeled and unlabeled data on a directed graph
ICML '05 Proceedings of the 22nd international conference on Machine learning
Cycle-transitive comparison of independent random variables
Journal of Multivariate Analysis
ICML '06 Proceedings of the 23rd international conference on Machine learning
Training linear SVMs in linear time
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Statistical Comparisons of Classifiers over Multiple Data Sets
The Journal of Machine Learning Research
Learning Sparse Representations by Non-Negative Matrix Factorization and Sequential Cone Programming
The Journal of Machine Learning Research
Learning to rank: from pairwise approach to listwise approach
Proceedings of the 24th international conference on Machine learning
ROC analysis in ordinal regression learning
Pattern Recognition Letters
On the scalability of ordered multi-class ROC analysis
Computational Statistics & Data Analysis
The Journal of Machine Learning Research
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity
Fuzzy Sets and Systems
Cost-Sensitive learning of SVM for ranking
ECML'06 Proceedings of the 17th European conference on Machine Learning
A transitivity analysis of bipartite rankings in pairwise multi-class classification
Information Sciences: an International Journal
Conditional ranking on relational data
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part II
Learning partial ordinal class memberships with kernel-based proportional odds models
Computational Statistics & Data Analysis
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The relationship between bipartite ranking algorithms, graph theory and ROC analysis has been formerly established with data sampled from two categories (i.e. classes). In this article, we discuss extensions for more general ranking models, with data sampled from, in general, r ordered categories. Similarly, such models can be visualized by means of a layered ranking graph in which each path in the graph corresponds to an r-tuple of correctly ranked objects with one object of each class. From an ROC analysis point of view, the fraction of correctly ranked r-tuples equals the volume under the ROC surface (VUS) for r ordered categories. Unlike the conventional kernel approach of minimizing the pairwise error, we try to optimize the fraction of correctly ranked r-tuples. A large number of constraints appear in the resulting quadratic program, but the optimal solution can be computed in O(n^3) time for samples of size n with structured support vector machines and graph-based techniques. Our approach can offer benefits for applications in various domains. On various synthetic and benchmark data sets, it outperforms the pairwise approach for balanced as well as unbalanced problems. In addition, scaling experiments confirm the theoretically derived time complexity.