Mathematics (Oct 2024)
Improving Hybrid Regularized Diffusion Processes with the Triple-Cosine Smoothness Constraint for Re-Ranking
Abstract
In the last few decades, diffusion processes have been widely used to solve visual re-ranking problems. The key point of these approaches is that, by diffusing the baseline similarities in the context of other samples, more reliable similarities or dissimilarities can be learned. This was later found to be achieved by solving the optimization problem underlying the framework of the regularized diffusion process. In this paper, the proposed model differs from previous approaches in two aspects. Firstly, by taking the high-order information of the graph into account, a novel smoothness constraint, named the triple-cosine smoothness constraint, is proposed. The triple-cosine smoothness constraint is generated using the cosine of the angle between the vectors in the coordinate system, which is created based on a group of three elements: the queries treated as a whole and two other data points. A hybrid fitting constraint is also introduced into the proposed model. It consists of two types of predefined values, which are, respectively, used to construct two types of terms: the squared L2 norm and the L1 norm. Both the closed-form solution and the iterative solution of the proposed model are provided. Secondly, in the proposed model, the learned contextual dissimilarities can be used to describe “one-to-many” relationships, making it applicable to problems with multiple queries, which cannot be solved by previous methods that only handle “one-to-one” relationships. By taking advantage of these “one-to-many” contextual dissimilarities, an iterative re-ranking process based on the proposed model is further provided. Finally, the proposed algorithms are validated on various databases, and comprehensive experiments demonstrate that retrieval results can be effectively improved using our methods.
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