ADMM-based online spectral hashing with elastic metric for cross-modal retrieval

Cross-modal retrieval establishes correspondence for information across heterogeneous modalities, such as searching images based on textual queries. Online cross-modal hashing technique has attracted research interest due to its fast retrieval speed, low storage costs, and ability to process streaming data. However, two critical limitations persist in existing online hashing retrieval approaches. First, the widespread use of the squared loss in hashing models treats all samples equally, resulting in low discrimination and robustness to inferior samples. Second, conventional hashing methods learn continuous features and acquire binary codes through the discretization mapping, which reduces the accuracy of representing cross-modal instances. To address these limitations, we propose a novel unsupervised online cross-modal hashing retrieval method, which introduces two key innovations: (1) we introduce an elastic norm to discriminate all training samples adaptively. This metric norm absorbs the $$\ell _1$$-norm and Frobenius norm by an adjustable coefficient, and it enhances the discriminability by adjusting the effect of the samples on the model; (2) we propose the cross-modal hashing with spectral embedding learning, such that the hash code grasps both linear and nonlinear relations among samples. An ADMM-based optimization scheme is designed to solve the hash code without the discretization mapping anymore. Extensive experimental results on MIRFlickr, NUS-WIDE, and IAPR TC datasets demonstrate the superiority of the proposed method against the relative competitors in the cross-modal retrieval task, specially achieving mAP@100 improvements of 6.9% on the NUS-WIDE dataset.