Learning contextual dissimilarity on tensor product graph for visual re-ranking

As the object retrieval problem cannot be well solved by pairwise distances, many algorithms have been developed for visual re-ranking as the post-processing step. As discussed in recent studies, the contextual similarity/dissimilarity based on diffusion process can be obtained by solving an optimization problem that contains a smoothness constraint and a fitting constraint. In this paper, we introduce the mean first-passage time (MFPT) as the contextual dissimilarity. By analysis of the principle behind MFPT, one can find that the corresponding cost function is generated with a hybrid fitting constraint, and the predefined values of contextual dissimilarities are limited within proper ranges. With the hybrid fitting constraint and the smoothness constraint based on a tensor product graph, we construct the objective function associated with a novel contextual dissimilarity. On that basis, we obtain the contextual dissimilarities as an iterative solution by solving the optimization problem, and the manifold structure can be effectively captured by using the proposed method. Our method is evaluated on retrieval tasks for different databases, and the re-ranking result with the proposed contextual dissimilarity outperforms other state-of-the-art algorithms.