Collective Affinity Learning for Partial Cross-Modal Hashing

In the past decade, various unsupervised hashing methods have been developed for cross-modal retrieval. However, in real-world applications, it is often the incomplete case that every modality of data may suffer from some missing samples. Most existing works assume that every object appears in both modalities, hence they may not work well for partial multi-modal data. To address this problem, we propose a novel Collective Affinity Learning Method (CALM), which collectively and adaptively learns an anchor graph for generating binary codes on partial multi-modal data. In CALM, we first construct modality-specific bipartite graphs collectively, and derive a probabilistic model to figure out complete data-to-anchor affinities for each modality. Theoretical analysis reveals its ability to recover missing adjacency information. Moreover, a robust model is proposed to fuse these modality-specific affinities by adaptively learning a unified anchor graph. Then, the neighborhood information from the learned anchor graph acts as feedback, which guides the previous affinity reconstruction procedure. To solve the formulated optimization problem, we further develop an effective algorithm with linear time complexity and fast convergence. Last, Anchor Graph Hashing (AGH) is conducted on the fused affinities for cross-modal retrieval. Experimental results on benchmark datasets show that our proposed CALM consistently outperforms the existing methods.