  Hierarchical semantic structures, naturally existing in real-world datasets,
can assist in capturing the latent distribution of data to learn robust hash
codes for retrieval systems. Although hierarchical semantic structures can be
simply expressed by integrating semantically relevant data into a high-level
taxon with coarser-grained semantics, the construction, embedding, and
exploitation of the structures remain tricky for unsupervised hash learning. To
tackle these problems, we propose a novel unsupervised hashing method named
Hyperbolic Hierarchical Contrastive Hashing (HHCH). We propose to embed
continuous hash codes into hyperbolic space for accurate semantic expression
since embedding hierarchies in hyperbolic space generates less distortion than
in hyper-sphere space and Euclidean space. In addition, we extend the K-Means
algorithm to hyperbolic space and perform the proposed hierarchical hyperbolic
K-Means algorithm to construct hierarchical semantic structures adaptively. To
exploit the hierarchical semantic structures in hyperbolic space, we designed
the hierarchical contrastive learning algorithm, including hierarchical
instance-wise and hierarchical prototype-wise contrastive learning. Extensive
experiments on four benchmark datasets demonstrate that the proposed method
outperforms the state-of-the-art unsupervised hashing methods. Codes will be
released.
