Hetero-manifold regularisation for cross-modal hashing

Recently, cross-modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi-modal data. To address both challenges, in this paper, we propose a novel method termed hetero-manifold regularisation (HMR) to supervise the learning of hash functions for efficient cross-modal search. A hetero-manifold integrates multiple sub-manifolds defined by homogeneous data with the help of cross-modal supervision information. Taking advantages of the hetero-manifold, the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero-manifold. Furthermore, a novel cumulative distance inequality defined on the hetero-manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes. By using the inequality, cross-modal hashing is transformed into a problem of hetero-manifold regularised support vector learning. Therefore, the performance of cross-modal search can be significantly improved by seamlessly combining the integrated information of the hetero-manifold and the strong generalisation of the support vector machine. Comprehensive experiments show that the proposed HMR achieve advantageous results over the state-of-the-art methods in several challenging cross-modal tasks.