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One major assumption used in most existing hashing approaches is that the domain of interest (i.e., the target domain) could provide sufficient training data, either labeled or unlabeled. However, this assumption may be violated in practice. To address this so-called data sparsity issue in hashing, a new framework termed transfer hashing with privileged information (THPI) is proposed, which marriages hashing and transfer learning (TL). To show the efficacy of THPI, we propose three variants of the well-known iterative quantization (ITQ)as a showcase. The proposed methods, ITQ+, LapITQ+, and deep transfer hashing (DTH), solve the aforementioned data sparsity issue from different aspects. Specifically, ITQ+ is a shallow model, which makes ITQ achieve hashing in a TL manner. ITQ+ learns a new slack function from the source domain to approximate the quantization error on the target domain given by ITQ. To further improve the performance of ITQ+, LapITQ+ is proposed by embedding the geometric relationship of the source domain into the target domain. Moreover, DTH is proposed to show the generality of our framework by utilizing the powerful representative capacity of deep learning. To the best of our knowledge, this could be one of the first DTH works. Extensive experiments on several popular data sets demonstrate the effectiveness of our shallow and DTH approaches comparing with several state-of-the-art hashing approaches. [ABSTRACT FROM AUTHOR]