Known for efficient computation and easy storage, hashing has been extensively explored in cross-modal retrieval. The majority of current hashing models are predicated on the premise of a direct one-to-one mapping between data points. However, in real practice, data correspondence across modalities may be partially provided. In this research, we introduce an innovative unsupervised hashing technique designed for semi-paired cross-modal retrieval tasks, named Reconstruction Relations Embedded Hashing (RREH). RREH assumes that multi-modal data share a common subspace. For paired data, RREH explores the latent consistent information of heterogeneous modalities by seeking a shared representation. For unpaired data, to effectively capture the latent discriminative features, the high-order relationships between unpaired data and anchors are embedded into the latent subspace, which are computed by efficient linear reconstruction. The anchors are sampled from paired data, which improves the efficiency of hash learning. The RREH trains the underlying features and the binary encodings in a unified framework with high-order reconstruction relations preserved. With the well devised objective function and discrete optimization algorithm, RREH is designed to be scalable, making it suitable for large-scale datasets and facilitating efficient cross-modal retrieval. In the evaluation process, the proposed is tested with partially paired data to establish its superiority over several existing methods.

翻译：哈希方法以其高效计算和易于存储的特点，在跨模态检索领域得到了广泛探索。当前大多数哈希模型都基于数据点之间存在直接一对一映射的前提。然而，在实际应用中，跨模态的数据对应关系可能仅被部分提供。本研究提出了一种创新的无监督哈希技术，专为半配对跨模态检索任务设计，称为重构关系嵌入哈希（RREH）。RREH假设多模态数据共享一个公共子空间。对于配对数据，RREH通过寻找共享表示来探索异构模态的潜在一致信息。对于非配对数据，为了有效捕获潜在的判别性特征，将非配对数据与锚点之间的高阶关系嵌入到潜在子空间中，这些关系通过高效的线性重构计算得出。锚点从配对数据中采样，这提高了哈希学习的效率。RREH在一个统一框架中训练底层特征和二进制编码，同时保持高阶重构关系。通过精心设计的目标函数和离散优化算法，RREH被设计为可扩展的，使其适用于大规模数据集并促进高效的跨模态检索。在评估过程中，所提出的方法使用部分配对数据进行测试，以证明其优于多种现有方法。