The hashing-based approximate nearest neighbors search is able to reduce the storage cost and improve query speed. Therefore, they have attracted much attention in these years. Moreover, some hashing methods have been proposed for cross-modal retrieval tasks. However, there are still some issues that need to be further addressed. For example, some of them only construct a simple similarity matrix when learning hash functions or binary codes, which may lose some useful information. Some of them solve the hard discrete optimization problem by relaxing the binary constraints and quantizing the solution to obtain the final results, which may generate large quantization errors. To address these challenges, we present a new supervised cross-modal hashing method, named supervised robust discrete multimodal hashing (SRDMH). Specifically, it incorporates full label information into the hash functions learning to preserve the similarity in the original space. In addition, instead of relaxing the binary constraints, it is able to learn the binary codes and hash functions simultaneously. Moreover, it adopts a flexible ℓ2,ploss with nonlinear kernel embedding and introduces an intermediate presentation of the binary codes. In light of this, it becomes more robust and easier to solve by an iterative algorithm presented in this paper. To evaluate its performance, we conduct extensive experiments on three benchmark datasets. The results verify that SRDMH outperforms seven state-of-the-art cross-modal hashing methods. In addition, we also extend it to the classification task. Compared with other hashing methods, SRDMH also obtains better results when its binary codes are used for classification.

Recently, multimodal hashing techniques have received considerable attention due to their low storage cost and fast query speed for multimodal data retrieval. Many methods have been proposed; however, there are still some problems that need to be further considered. For example, some of these methods just use a similarity matrix for learning hash functions which will discard some useful information contained in original data; some of them relax binary constraints or separate the process of learning hash functions and binary codes into two independent stages to bypass the obstacle of handling the discrete constraints on binary codes for optimization, which may generate large quantization error; some of them are not robust to noise. All these problems may degrade the performance of a model. To consider these problems, in this paper, we propose a novel supervised hashing framework for cross-modal retrieval, i.e., Supervised Robust Discrete Multimodal Hashing (SRDMH). Specifically, SRDMH tries to make final binary codes preserve label information as same as that in original data so that it can leverage more label information to supervise the binary codes learning. In addition, it learns hashing functions and binary codes directly instead of relaxing the binary constraints so as to avoid large quantization error problem. Moreover, to make it robust and easy to solve, we further integrate a flexible l2,p loss with nonlinear kernel embedding and an intermediate presentation of each instance. Finally, an alternating algorithm is proposed to solve the optimization problem in SRDMH. Extensive experiments are conducted on three benchmark data sets. The results demonstrate that the proposed method (SRDMH) outperforms or is comparable to several state-of-the-art methods for cross-modal retrieval task.