Robust and Flexible Discrete Hashing for Cross-Modal Similarity Search

Multimodal hashing approaches have gained great success on large-scale cross-modal similarity search applications, due to their appealing computation and storage efficiency. However, it is still a challenge work to design binary codes to represent the original features with good performance in an unsupervised manner. We argue that there are some limitations that need to be further considered for unsupervised multimodal hashing: 1) most existing methods drop the discrete constraints to simplify the optimization, which will cause large quantization error; 2) many methods are sensitive to outliers and noises since they use ℓ ₂ -norm in their objective functions which can amplify the errors; and 3) the weight of each modality, which greatly influences the retrieval performance, is manually or empirically determined and may not fully fit the specific training set. The above limitations may significantly degrade the retrieval accuracy of unsupervised multimodal hashing methods. To address these problems, in this paper, a novel hashing model is proposed to efficiently learn robust discrete binary codes, which is referred as Robust and Flexible Discrete Hashing (RFDH). In the proposed RFDH model, binary codes are directly learned based on discrete matrix decomposition, so that the large quantization error caused by relaxation is avoided. Moreover, the ℓ _2,1 -norm is used in the objective function to improve the robustness, such that the learned model is not sensitive to data outliers and noises. In addition, the weight of each modality is adaptively adjusted according to training data. Hence the important modality will get large weights during the hash learning procedure. Owing to above merits of RFDH, it can generate more effective hash codes. Besides, we introduce two kinds of hash function learning methods to project unseen instances into hash codes. Extensive experiments on several well-known large databases demonstrate superior performance of the proposed hash model over most state-of-the-art unsupervised multimodal hashing methods.