Affinity learning on a tensor product graph with applications to shape and image retrieval

As observed in several recent publications, improved retrieval performance is achieved when pairwise similarities between the query and the database objects are replaced with more global affinities that also consider the relation among the database objects. This is commonly achieved by propagating the similarity information in a weighted graph representing the database and query objects. Instead of propagating the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. By virtue of this construction, not only local but also long range similarities among graph nodes are explicitly represented as higher order relations, making it possible to better reveal the intrinsic structure of the data manifold. In addition, we improve the local neighborhood structure of the original graph in a preprocessing stage. We illustrate the benefits of the proposed approach on shape and image ranking and retrieval tasks. We are able to achieve the bull´s eye retrieval score of 99.99% on MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms.