Adaptive Distances on Sets of Vectors

Recently, there has been a growing interest in learning distances directly from training data. While the previous works focused mainly on adapting distance measures over vectorial data, it is a well-known fact that many real-world data could not be easily represented as fixed length tuples of constants. In this paper we address this limitation and propose a novel class of distance learning techniques for learning problems in which instances are set of vectors, examples of such problems include, among others, automatic image annotation and graph classification. We investigate the behavior of the adaptive set distances on a number of artificial and real-world problems and demonstrate that they improve over the standard set distances.