Support vector learning for ordinal regression

"Support vector learning for ordinal regression," R. Herbrich, ICANN, 1999.

This paper proposes a new learning task for ordinal regression which is complementary to both classification and metric regression because of discrete and ordered outcome space. The formulation for this task is to formalize as a problem of binary classification by minimizing pairwise 0-1 loss.

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where U is the rank function to output the score.

Here below is an toy example from this paper, the figure(b) is the mapping result for figure(a), and after mapping, we can simply find the margin.

This paper considers the simply concept of SVM, and uses it for ranking. Although inefficiency and not-so-good accuracy, it's still a guide for us to think about ranking problems.