Unsupervised cross-modal hashing is a topic of considerable interest due to its advantages in terms of low storage costs and fast retrieval speed. Despite the impressive achievements of existing solutions, two challenges remain unaddressed: (1) Semantic similarity obtained without supervision is not accurate enough, and (2) the preservation of similarity structures lacks effectiveness due to the neglect of both global and local similarity. This paper introduces a new method, Multi-Grained Similarity Preserving and Updating (MGSPU), to tackle these challenges. To overcome the first challenge, M...