Abstract: Aiming at  the isotropy problem caused by the widespread use of cosine metrics in proxy-based deep metric learning methods, we  proposed a deep metric learning method that integrated Euclidean geometry and hyperbolic geometry. By introducing hyperbolic geometry with advantages in hierarchical modeling,  a local hyperbolic loss function was designed in hyperbolic space, and  the distribution prior of hyperbolic space was used to initialize proxy points reasonably. During training process, the local neighborhood proxy points corresponding to each sample were dynamically optimized, thereby effectively enhancing the inter-class discriminative ability of the model in local regions. Experimental results show that the proposed method exhibits significant performance improvements on multiple standard image retrieval datasets, thus validating the effectiveness of blending different geometric 
properties for enhancing discriminative performance in metric learning.

Key words: deep metric learning, hyperbolic geometry, image retrieval, computer vision