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Diffusion process has advanced object retrieval greatly as it can capture the underlying manifold structure. Recent studies have experimentally demonstrated that tensor product diffusion can better reveal the intrinsic relationship between objects than other variants. However, the principle remains unclear, i.e., what kind of manifold structure is captured. In this paper, we propose a new affinity learning algorithm called Regularized Diffusion Process (RDP). By deeply exploring the properties of RDP, our first yet basic contribution is providing a manifold-based explanation for tensor product diffusion. A novel criterion measuring the smoothness of the manifold is defined, which simultaneously regularizes four vertices in the affinity graph. Inspired by this observation, we further contribute two variants towards two specific goals. While ARDP can learn similarities across heterogeneous domains, HRDP performs affinity learning on tensor product hypergraph, considering the relationships between objects are generally more complex than pairwise. Consequently, RDP, ARDP and HRDP constitute a generic tool for object retrieval in most commonly-used settings, no matter the input relationships between objects are derived from the same domain or not, and in pairwise formulation or not. Comprehensive experiments on 10 retrieval benchmarks, especially on large scale data, validate the effectiveness and generalization of our work. [ABSTRACT FROM AUTHOR]

As a post-processing procedure, the diffusion process has demonstrated its ability of substantially improving the performance of various visual retrieval systems. Whereas, great efforts are also devoted to similarity (or metric) fusion, seeing that only one individual type of similarity cannot fully reveal the intrinsic relationship between objects. This stimulates a great research interest of considering similarity fusion in the framework of the diffusion process (i.e., fusion with diffusion) for robust retrieval. In this paper, we first revisit representative methods about fusion with diffusion and provide new insights which are ignored by previous researchers. Then, observing that existing algorithms are susceptible to noisy similarities, the proposed regularized ensemble diffusion (RED) is bundled with an automatic weight learning paradigm, so that the negative impacts of noisy similarities are suppressed. Though formulated as a convex optimization problem, one advantage of RED is that it converts back into the iteration-based solver with the same computational complexity as the conventional diffusion process. At last, we integrate several recently-proposed similarities with the proposed framework. The experimental results suggest that we can achieve new state-of-the-art performances on various retrieval tasks, including 3D shape retrieval on the ModelNet data set, and image retrieval on the Holidays and Ukbench data sets. [ABSTRACT FROM AUTHOR]