caa a22 4500 445839929 CHVBK 20180317145340.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00186-011-0368-z doi (NATIONALLICENCE)springer-10.1007/s00186-011-0368-z Maximizing upgrading and downgrading margins for ordinal regression [Elektronische Daten] [Emilio Carrizosa, Belen Martin-Barragan] In ordinal regression, a score function and threshold values are sought to classify a set of objects into a set of ranked classes. Classifying an individual in a class with higher (respectively lower) rank than its actual rank is called an upgrading (respectively downgrading) error. Since upgrading and downgrading errors may not have the same importance, they should be considered as two different criteria to be taken into account when measuring the quality of a classifier. In Support Vector Machines, margin maximization is used as an effective and computationally tractable surrogate of the minimization of misclassification errors. As an extension, we consider in this paper the maximization of upgrading and downgrading margins as a surrogate of the minimization of upgrading and downgrading errors, and we address the biobjective problem of finding a classifier maximizing simultaneously the two margins. The whole set of Pareto-optimal solutions of such biobjective problem is described as translations of the optimal solutions of a scalar optimization problem. For the most popular case in which the Euclidean norm is considered, the scalar problem has a unique solution, yielding that all the Pareto-optimal solutions of the biobjective problem are translations of each other. Hence, the Pareto-optimal solutions can easily be provided to the analyst, who, after inspection of the misclassification errors caused, should choose in a later stage the most convenient classifier. The consequence of this analysis is that it provides a theoretical foundation for a popular strategy among practitioners, based on the so-called ROC curve, which is shown here to equal the set of Pareto-optimal solutions of maximizing simultaneously the downgrading and upgrading margins. Springer-Verlag, 2011 Multi objective optimization nationallicence Support Vector Machines nationallicence Ordinal regression nationallicence Carrizosa Emilio Facultad de Matemáticas, Universidad de Sevilla (Spain), Avda. Reina Mercedes, s/n, 41012, Sevilla, Spain aut Martin-Barragan Belen Facultad de CCSSJJ, Universidad Carlos III de Madrid (Spain), c/Madrid, 126, 28903, Getafe, Madrid, Spain aut Mathematical Methods of Operations Research Springer-Verlag 74/3(2011-12-01), 381-407 1432-2994 74:3<381 2011 74 186 https://doi.org/10.1007/s00186-011-0368-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-011-0368-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carrizosa Emilio Facultad de Matemáticas, Universidad de Sevilla (Spain), Avda. Reina Mercedes, s/n, 41012, Sevilla, Spain aut NATIONALLICENCE 700 1- Martin-Barragan Belen Facultad de CCSSJJ, Universidad Carlos III de Madrid (Spain), c/Madrid, 126, 28903, Getafe, Madrid, Spain aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 74/3(2011-12-01), 381-407 1432-2994 74:3<381 2011 74 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer