Unsupervised hashing based on the recovery of subspace structures

Zhibao Tian, Hui Zhang, Yong Chen, Dell Zhang

Abstract: Highlights • Our method adapts the LRR model into a new variant, based on which the learned correlation matrix could be designed into a space-and-time saving formula for data semantics. • To tackle the discrete graph hashing, we presents a new learning method, i.e., transforms the original optimization problem into three subproblems by means of surrogate variables, and most importantly each subproblem is addressed with a closed-form solution, which makes the whole hashing learning converge within dozens of iterations. • Experiments on four datasets demonstrate the advantages of our method over several state-of- the-art unsupervised hashing models including two recently proposed unsupervised deep hashing methods. Abstract Unsupervised semantic hashing should in principle keep the semantics among samples consistent with the intrinsic geometric structures of the dataset. In this paper, we propose a novel multiple stage unsupervised hashing method, named “ Unsupervised Hashing based on the Recovery of Subspace Structures ” (RSSH) for image retrieval. Specifically, we firstly adapt the Low-rank Representation (LRR) model into a new variant which treats the real-world data as samples drawn from a union of several low-rank subspaces. Then, the pairwise similarities are represented in a space-and-time saving manner based on the learned low-rank correlation matrix of the modified LRR. Next, the challenging discrete graph hashing is employed for binary hashing codes. Notably, we convert the original graph hashing model into an optimization-friendly formalization, which is addressed with efficient closed-form solutions for its subproblems. Finally, the devised linear hash functions are fast achieved for out-of-samples. Retrieval experiments on four image datasets testify the superiority of RSSH to several state-of-the-art hashing models. Besides, it’s worth mentioning that RSSH, a shallow model, significantly outperforms two recently proposed unsupervised deep hashing methods, which further confirms its effectiveness.