Hierarchical ranking in hyperbolic space: A novel approach to metric learning.

The integration of deep metric learning with hyperbolic geometry has shown significant potential for capturing complex hierarchical relationships. However, existing clustering-based methods struggle to fully leverage the properties of hyperbolic space, particularly due to the challenge of optimizing both cluster centers and distance metrics in exponentially expanding spaces without true hierarchical labels. Additionally, the computational complexity of Riemannian operations makes maintaining hierarchical structures costly, especially for large datasets. To address these challenges, we propose a novel hierarchical ranking framework that utilizes latent hierarchical information without relying on explicit clustering. This framework introduces the Hierarchical Ranking Generation (HRG) strategy and Hierarchical Ranking Loss (HRL). HRG generates ranking labels based on the semantic relationships between classes within an implicit global hierarchy, while HRL optimizes these rankings across multiple hierarchical levels, enabling the model to learn richer, more nuanced representations. Our approach significantly improves performance, outperforming the state-of-the-art by 2.4% on CUB-200-2011 and 1.6% on Cars-196 at Recall@1.