Hybrid Regularization of Diffusion Process for Visual Re-Ranking

To improve the retrieval result obtained from a pairwise dissimilarity, many variants of diffusion process have been applied in visual re-ranking. In the framework of diffusion process, various contextual similarities can be obtained by solving an optimization problem, and the objective function consists of a smoothness constraint and a fitting constraint. And many improvements on the smoothness constraint have been made to reveal the underlying manifold structure. However, little attention has been paid to the fitting constraint, and how to build an effective fitting constraint still remains unclear. In this article, by deeply analyzing the role of fitting constraint, we firstly propose a novel variant of diffusion process named Hybrid Regularization of Diffusion Process (HyRDP). In HyRDP, we introduce a hybrid regularization framework containing a two-part fitting constraint, and the contextual dissimilarities can be learned from either a closed-form solution or an iterative solution. Furthermore, this article indicates that the basic idea of HyRDP is closely related to the mechanism behind Generalized Mean First-passage Time (GMFPT). GMFPT denotes the mean time-steps for the state transition from one state to any one in the given state set, and is firstly introduced as the contextual dissimilarity in this article. Finally, based on the semi-supervised learning framework, an iterative re-ranking process is developed. With this approach, the relevant objects on the manifold can be iteratively retrieved and labeled within finite iterations. The proposed algorithms are validated on various challenging databases, and the experimental performances demonstrate that retrieval results obtained from different types of measures can be effectively improved by using our methods.