Cross-modal hashing has recently attracted considerable attention in the large-scale retrieval task due to its low storage cost and high retrieval efficiency. However, the existing hashing methods still have some issues that need to be further solved. For example, most existing cross-modal hashing methods convert the original data into a common Hamming space to learn unified hash codes, which ignores the specific properties of multi-modal data. In addition, most of them relax the discrete constraint to learn hash codes, which may lead to quantization loss and suboptimal performance. In order to address the above problems, this paper proposes a novel cross-modal retrieval method, named discrete matrix factorization hashing (DMFH). DMFH is a two-stage approach. In the first stage, given training data, DMFH exploits the matrix factorization technique to learn modality-specific semantic representation for each modality, then generates the corresponding hash codes by linear projection. Meanwhile, in order to ensure that the hash codes can preserve the semantic similarity between different modalities, DMFH optimizes the hash codes by an affinity matrix constructed from the label information. During the first stage, DMFH proposes a discrete optimal algorithm to solve the discrete constraint problem in learning hash codes. In the second stage, given the hash codes learned in the first stage, DMFH utilizes kernel logistic regression to learn the nonlinear features from the unseen instance, then generates corresponding hash codes for each modality. Extensive experimental results on three public benchmark datasets show that the proposed DMFH outperforms several state-of-art cross-modal hashing methods in terms of accuracy and efficiency.

由于其低存储成本和高检索效率，跨模态哈希最近在大规模检索任务中引起了相当大的关注。但是，现有的哈希方法仍然存在一些需要进一步解决的问题。例如，大多数现有的跨模态哈希方法将原始数据转换为公共汉明空间来学习统一的哈希码，而忽略了多模态数据的特定属性。此外，他们中的大多数人放松了离散约束来学习哈希码，这可能会导致量化损失和次优性能。为了解决上述问题，本文提出了一种新的跨模态检索方法，称为离散矩阵分解散列（DMFH）。DMFH 是一个两阶段的方法。在第一阶段，给定训练数据，DMFH 利用矩阵分解技术为每个模态学习模态特定的语义表示，然后通过线性投影生成相应的哈希码。同时，为了保证哈希码能够保留不同模态之间的语义相似性，DMFH通过根据标签信息构建的亲和度矩阵来优化哈希码。在第一阶段，DMFH 提出了一种离散最优算法来解决学习哈希码中的离散约束问题。在第二阶段，给定在第一阶段学习的哈希码，DMFH 利用核逻辑回归从看不见的实例中学习非线性特征，然后为每个模态生成相应的哈希码。