Asymmetric Binary Coding for Image Search.

Learning to hash has attracted broad research interests in recent computer vision and machine learning studies, due to its ability to accomplish efficient approximate nearest neighbor search. However, the closely related task, maximum inner product search (MIPS), has rarely been studied in this literature. To facilitate the MIPS study, in this paper, we introduce a general binary coding framework based on asymmetric hash functions, named asymmetric inner-product binary coding (AIBC). In particular, AIBC learns two different hash functions, which can reveal the inner products between original data vectors by the generated binary vectors. Although conceptually simple, the associated optimization is very challenging due to the highly nonsmooth nature of the objective that involves sign functions. We tackle the nonsmooth optimization in an alternating manner, by which each single coding function is optimized in an efficient discrete manner. We also simplify the objective by discarding the quadratic regularization term which significantly boosts the learning efficiency. Both problems are optimized in an effective discrete way without continuous relaxations, which produces high-quality hash codes. In addition, we extend the AIBC approach to the supervised hashing scenario, where the inner products of learned binary codes are forced to fit the supervised similarities. Extensive experiments on several benchmark image retrieval databases validate the superiority of the AIBC approaches over many recently proposed hashing algorithms.