Supervised Consensus Anchor Graph Hashing for Cross Modal Retrieval

Cross–modal hashing has gained significant attention due to its efficient computational capabilities and impressive retrieval performance. Most supervised methods rely on the auxiliary learning of a similarity matrix, which incurs computational and storage expenses with a complexity of
$O(n^{2})$
. By capturing the adjacency relationships between anchor points and original data, the anchor graph learning strategy effectively reduces the time complexity. However, existing anchor graph hashing methods adopt heuristic sampling strategies like k–means or random sampling to determine anchor points. Unfortunately, this approach separates from the anchor graph construction and fails to accurately capture the fine–grained similarity relationships. To overcome this limitation, we introduce a novel method called supervised consensus anchor graph hashing (SCAGH) for cross–modal retrieval with linear complexity. In SCAGH, the anchor points are automatically selected and consensus anchor graph learning is integrated in an unified framework. Through mutual collaboration, a more fine–grained and discriminative consensus anchor graph can be obtained without extra hyper–parameters. Additionally, we utilize anchor graph matrix to approximate the pairwise similarity matrix so that the high complexity can be avoided and enhance the quality of hash codes. Extensive experiments on four benchmark datasets are conducted to verify the superiority of the proposed SCAGH compared to several state–of–the–art methods.