Learning a Distance Metric from Relative Comparisons

This paper presents a method for learning a distance metric from relative comparisonsuch as "A is closer to B than A is to C". Taking a Support Vector Machine (SVM) approach, we develop an algorithm that provides a flexible way of describing qualitative training data as a set of constraints. We show that such constraints lead to a convex quadratic programming problem that can be solved by adapting standard methods forSVM training. We empirically evaluate the performance and the modelling flexibility of the algorithm on a collection of text documents.