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       author = {Brinker, Klaus and F{\"{u}}rnkranz, Johannes and H{\"{u}}llermeier, Eyke},
        title = {Label Ranking by Learning Pairwise Preferences},
       number = {TUD-KE-2007-01},
         year = {2007},
  institution = {TU Darmstadt, Knowledge Engineering Group},
          url = {http://www.ke.informatik.tu-darmstadt.de/publications/reports/tud-ke-2007-01.pdf},
     abstract = {Preference learning is a challenging problem that involves the prediction of complex
structures, such as weak or partial order relations. In the recent literature, the problem
appears in many different guises, which we will first put into a coherent framework. This
work then focuses on a particular learning scenario called label ranking, where the problem
is to learn a mapping from instances to rankings over a finite number of labels. Our approach
for learning such a ranking function, ranking by pairwise comparison (RPC), first
induces a binary preference relation from suitable training data using a natural extension
of pairwise classification. A ranking is then derived from the learned relation by means
of a ranking procedure, whereby different ranking methods can be used for minimizing
different loss functions. In particular, we show that (weighted) voting as a rank aggregation
technique minimizes the Spearman rank correlation. Finally, we compare RPC to
constraint classification, an alternative approach to label ranking, and show empirically
and theoretically that RPC is computationally more efficient.}