Ranking with Large Margin Principle: Two Approaches

We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized - which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to lI-SVM when the number of classes k = 2. Both approaches are optimal in size of 21 where I is the total number of training examples. Experiments performed on visual classification and "collaborative filtering" show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.