Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been recently developed, compared to the conventional Euclidean embedding in most of the previously developed models, and can be more effective in representing the hierarchical data structure. Second, uncertainty estimation/measurement is a long-lasting challenge in artificial intelligence. Successful uncertainty estimation can improve a machine learning model's performance, robustness, and security. In Hyperbolic space, uncertainty measurement is at least with equivalent, if not more, critical importance. In this paper, we develop a Hyperbolic image embedding with uncertainty-aware metric learning for image retrieval. We call our method Hyp-UML: Hyperbolic Uncertainty-aware Metric Learning. Our contribution are threefold: we propose an image embedding algorithm based on Hyperbolic space, with their corresponding uncertainty value; we propose two types of uncertainty-aware metric learning, for the popular Contrastive learning and conventional margin-based metric learning, respectively. We perform extensive experimental validations to prove that the proposed algorithm can achieve state-of-the-art results among related methods. The comprehensive ablation study validates the effectiveness of each component of the proposed algorithm.

翻译：度量学习在训练图像检索与分类中发挥着关键作用，同时也是表示学习的核心算法之一，例如在特征学习及其度量空间对齐中。与先前大多数模型采用的欧几里得嵌入相比，近期发展的双曲嵌入在表示层次化数据结构方面更具优势。其次，不确定性估计/测量是人工智能领域的长期挑战。成功的不确定性估计能够提升机器学习模型的性能、鲁棒性与安全性。在双曲空间中，不确定性测量的重要性至少与欧几里得空间相当，甚至更为关键。本文提出了一种面向图像检索的、融合不确定性感知度量学习的双曲图像嵌入方法，命名为Hyp-UML（双曲不确定性感知度量学习）。我们的贡献包括三方面：提出基于双曲空间的图像嵌入算法及其对应的不确定性值；针对流行的对比学习与传统的基于边界的度量学习，分别提出两种类型的不确定性感知度量学习。通过大量实验验证，所提算法在相关方法中取得了最先进的结果。全面的消融研究验证了算法各组件的有效性。