"Learning to rank" is automatically creating a ranking function that assigns scores to instances, then rank the instances by using the scores.
This paper formalizes learning to rank as a problem of binary classification, and uses SVM (support vector machine) to learn the binary classifier. This formulation minimizes pair-wise 0-1 loss.
The learned ranking function can be viewed as (1)Ranking function: given an example, output its ranking score. (2)Classifier: given a pair of instances, output their relative ranking.
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