WITHDRAWN: SCHEMA: A Discrete Cross-Modal Hashing by Preserving Multiple Similarities

Abstract

Abstract Recently, cross-modal hashing has attracted much attention. To learn hash codes, many supervised cross-modal hashing methods construct a large-size semantic pairwise similarity matrix and reconstruct it by hash codes, which is time-consuming and neglects the similarity between high-level and low-level features. In addition, the binary constraints of hash codes make the optimization problem NP-hard. Most methods relax the binary constraints, leading to large quantization error. To address these issues, in this paper, we present a novel cross-modal hashing method, i.e., diScrete Cross-modal Hashing by prEserving Multiple similArities, SCHEMA for short. It embeds multiple types of similarity into the learning of binary codes, i.e., the high-level similarity and the low-level similarity. In the light of this, the binary codes may preserve more similarity information of the samples in the original space. In addition, to solve the optimization problem, it equivalently transforms the binary constraints into an intersection of two continuous spaces. Thereafter, the problem is solved with a proposed algorithm without relaxation, avoiding the large quantization error problem. Moreover, the computational complexity of its training is linear to the size of a training set, making it scalable to large-scale datasets. Extensive experimental results on four benchmark datasets demonstrate SCHEMA consistently outperforms some state-of-the-art hashing methods by large gaps.