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.

中文翻译：

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用于对象检索的双向上下文正则化扩散过程

扩散过程具有先进的对象检索功能，因为它可以捕获底层的流形结构。最近的研究通过实验证明，张量积扩散比其他变体可以更好地揭示对象之间的内在联系。但是，原理仍然不清楚，即捕获了哪种歧管结构。在本文中，我们提出了一种新的亲和力学习算法，称为正则扩散过程（RDP）。通过深入探索RDP的特性，我们的第一个基本贡献就是为张量积的扩散提供基于流形的解释。定义了测量流形平滑度的新标准，该标准同时对亲和图中的四个顶点进行了正则化。受此观察启发，我们进一步朝着两个具体目标贡献了两个变体。尽管ARDP可以学习跨异构域的相似性，但是HRDP在张量积超图上执行亲和力学习，考虑到对象之间的关系通常比成对复杂。因此，RDP，ARDP和HRDP构成了在大多数常用设置中进行对象检索的通用工具，无论对象之间的输入关系是否来自同一域，以及是否成对表达。在10个检索基准上，特别是在大规模数据上的综合实验，验证了我们工作的有效性和普遍性。无论对象之间的输入关系是否来自相同的域，以及是否成对表达，ARDP和HRDP都是在大多数常用设置中用于对象检索的通用工具。在10个检索基准上，特别是在大规模数据上的综合实验，验证了我们工作的有效性和普遍性。无论对象之间的输入关系是否来自相同的域，以及是否成对表达，ARDP和HRDP都是在大多数常用设置中用于对象检索的通用工具。在10个检索基准上，特别是在大规模数据上的综合实验，验证了我们工作的有效性和普遍性。