This paper proposes a novel method, Enhanced Discrete Multi-modal Hashing (EDMH), which learns binary codes and hash functions simultaneously from the pairwise similarity matrix of data for large-scale cross-view retrieval. EDMH distinguishes itself from existing methods by considering not just the binarization constraint but also the balance and decorrelation constraints. Although those additional discrete constraints make the optimization problem of EDMH look a lot more complicated, we are actually able to develop a fast iterative learning algorithm in the alternating optimization framework for it, as after introducing a couple of auxiliary variables each subproblem of optimization turns out to have closed-form solutions. It has been confirmed by extensive experiments that EDMH can consistently deliver better retrieval performances than state-of-the-art MH methods at lower computational costs.

Due to the exponential growth of multimedia data, multi-modal hashing as a promising technique to make cross-view retrieval scalable is attracting more and more attention. However, most of the existing multi-modal hashing methods either divide the learning process unnaturally into two separate stages or treat the discrete optimization problem simplistically as a continuous one, which leads to suboptimal results. Recently, a few discrete multi-modal hashing methods that try to address such issues have emerged, but they still ignore several important discrete constraints (such as the balance and decorrelation of hash bits). In this paper, we overcome those limitations by proposing a novel method named “Enhanced Discrete Multi-modal Hashing (EDMH)” which learns binary codes and hashing functions simultaneously from the pairwise similarity matrix of data, under the aforementioned discrete constraints. Although the model of EDMH looks a lot more complex than the other models for multi-modal hashing, we are actually able to develop a fast iterative learning algorithm for it, since the subproblems of its optimization all have closed-form solutions after introducing a couple of auxiliary variables. Our experimental results on three real-world datasets have revealed the usefulness of those previously ignored discrete constraints and demonstrated that EDMH not only performs much better than state-of-the-art competitors according to several retrieval metrics but also runs much faster than most of them.

Learning to hash is a fundamental technique widely used in large-scale image retrieval. Most existing methods for learning to hash address the involved discrete optimization problem by the continuous relaxation of the binary constraint, which usually lead to large quantization errors and consequently suboptimal binary codes. A few discrete hashing methods have emerged recently. However, they either completely ignore some useful constraints (specifically the balance and decorrelation of hash bits) or just turn those constraints into regularizers that would make the optimization easier but less accurate. In this paper, we propose a novel supervised hashing method named, Strongly Constrained Discrete Hashing (SCDH), which overcomes such limitations. It can learn the binary codes for all examples in the training set, and meanwhile obtain a hash function for unseen samples with the above mentioned constraints preserved. Although the model of SCDH is fairly sophisticated, we are able to find closed-form solutions to all of its optimization subproblems and thus design an efficient algorithm that converges quickly. In addition, we extend SCDH to a kernelized version SCDHK. Our experiments on three large benchmark datasets have demonstrated that not only can SCDH and SCDHK achieve substantially higher MAP scores than state-of-the-art baselines, but they run much faster than those that are also supervised as well.