# Proxy-Based Semi-Supervised Cross-Modal Hashing
## 1 Introduction  
With the exponential growth of multimedia data on the internet, the ability to efficiently search for and retrieve relevant information has become a crucial task. Deep cross-modal hashing, which maps different modalities (e.g., images, text, and videos) into a common low-dimensional space, has emerged as a powerful solution for fast and efficient retrieval [1, 2, 3, 4, 5, 6, 7, 8, 9]. This technique enables the use of binary codes to represent data, making retrieval both fast and scalable. However, the effectiveness of cross-modal hashing methods often relies on the availability of large amounts of labeled data for training, which is not always feasible in real-world applications [10, 11, 12, 13]. Due to the difficulty in obtaining labeled data, especially for large-scale datasets, semi-supervised learning techniques have gained increasing attention in the field of cross-modal retrieval. These methods aim to leverage both labeled and unlabeled data, reducing the reliance on expensive and time-consuming manual labeling processes. Semi-supervised learning seeks to effectively utilize the wealth of unlabeled data, which are often more abundant and easier to collect, while maximizing the information extracted from the relatively smaller labeled dataset. By incorporating both labeled and unlabeled data into the training process, these approaches have shown great potential for improving retrieval performance in scenarios where labeled data are scarce [14, 15, 16]. Motivation. The existing semi-supervised cross-modal hashing retrieval methods focus on exploring the similarity relationships between different modalities, aiming to map similar data closer together and dissimilar data farther apart in a shared low-dimensionalspace while preserving these relationships [17; 18]. However, they often neglect the \"data-category\" relationships, which leads to suboptimal retrieval performance. Moreover, these methods primarily concentrate on generating high-quality discrete pseudo-labels, overlooking the structural relationships between data and categories inherent in continuous pseudo-labels. For example, when predicting the pseudo-label of an unlabeled data sample A, a confidence distribution indicating its likelihood of belonging to certain categories is obtained. This distribution contains rich structural information about the relationships between data and categories. However, the existing methods fail to fully utilize this information, instead setting a threshold to discretize the continuous labels [19; 20; 21; 22]. Therefore, effectively leveraging the information within continuous pseudo-labels remains a significant challenge. Our Method. To answer the above questions, we proposed a novel Proxy-based Semi-Supervised Cross-modal Hashing (PSSCH) method for semi-supervised cross-modal retrieval. Our proposed method introduces a category proxy network (CPNet) and a novel Adaptive Dual-Label Loss to address the challenges in semi-supervised cross-modal hashing. The CPNet consists of two key components: feature proxies and hash proxies. Feature proxies are learned and updated based on labeled data features. Each proxy represents the category center point of a category in the feature space, providing a reliable basis for generating pseudo-labels for unlabeled data. Hash proxies represent category centers in the hash space and are obtained by forward-propagating the feature proxies. This process ensures that the hash proxies preserve the structural relationships between feature proxies in the feature space as much as possible in the hash space. By learning excellent feature proxies and hash proxies via the CPNet, we can consider both data-data and data-category relationships during model training. The Adaptive Dual-Label Loss is specifically designed to handle the differences between discrete ground truth labels (labeled data) and continuous pseudo-labels (unlabeled data). By adopting different learning strategies, it effectively optimizes both types of labels.