Efficient Rank-Based Diffusion Process with Assured Convergence

Visual features and representation learning strategies experienced huge advances in the previous decade, mainly supported by deep learning approaches. However, retrieval tasks are still performed mainly based on traditional pairwise dissimilarity measures, while the learned representations lie on high dimensional manifolds. With the aim of going beyond pairwise analysis, post-processing methods have been proposed to replace pairwise measures by globally defined measures, capable of analyzing collections in terms of the underlying data manifold. The most representative approaches are diffusion and ranked-based methods. While the diffusion approaches can be computationally expensive, the rank-based methods lack theoretical background. In this paper, we propose an efficient Rank-based Diffusion Process which combines both approaches and avoids the drawbacks of each one. The obtained method is capable of efficiently approximating a diffusion process by exploiting rank-based information, while assuring its convergence. The algorithm exhibits very low asymptotic complexity and can be computed regionally, being suitable to outside of dataset queries. An experimental evaluation conducted for image retrieval and person re-ID tasks on diverse datasets demonstrates the effectiveness of the proposed approach with results comparable to the state-of-the-art.