# Deep Class-Guided Hashing for Multi-Label Cross-Modal Retrieval
###### Abstract  
Deep hashing has gained widespread attention in cross-modal retrieval due to its low cost and efficient retrieval advantages. However, existing cross-modal hashing methods either focus solely on exploring relationships between data points--which inevitably leads to intra-class dispersion--or emphasize the relationships between data points and categories while neglecting the preservation of inter-class structural relationships, resulting in suboptimal hash codes. To address this issue, this paper proposes a Deep Class-Guided Hashing (DCGH) method, which approaches model learning from the category level. It ensures that data of the same category are clustered around the same class center while maintaining the structural relationships between class centers. Extensive comparative experiments conducted on three benchmark datasets demonstrate that the DCGH method achieves comparable or even superior performance compared to existing cross-modal retrieval methods. deep hashing; intra-class aggregation; inter-class structural relationships; semantic bias 2020  
\(\mathcal{L}_{pxy}\)[4; 20; 21; 22]. Center loss penalizes the distance between each sample and its corresponding class center, effectively clustering intra-class samples and promoting a more compact intra-class distribution. However, in multi-label scenarios, learning a stable center vector for each class remains challenging. Proxy loss-based methods mitigate this issue by introducing a proxy vector for each single-label category and learning the hash representation by minimizing the distance between samples and their corresponding proxies while maximizing the distance between samples and proxies from other categories. Notably, proxy-based hashing methods demonstrate remarkable generalization capabilities, particularly in handling unseen categories, as they shift the learning focus from modeling the relationships between samples to learning the relationships between samples and proxy vectors. Despite their advantages, however, as illustrated in Figure 1, these approaches also suffer from a significant drawback: they struggle to preserve the inter-class similarity structure. To simultaneously preserve intra-class and inter-class similarity structures, an intuitive approach is to combine \(\mathcal{L}_{pair}\) with \(\mathcal{L}_{pxy}\). However, constructing an optimal solution that leverages the advantages of both objectives presents significant challenges. Firstly, the semantic bias issue inevitably arises when considering the similarity relationships not only among data points themselves but also between data points and class proxies. This issue becomes particularly pronounced in scenarios where there are imbalances in the number of data points across different classes. Taking Figure 2 as an example, class \(\mathbf{s}_{1}\) is related to proxy points \(\mathbf{p}_{1}\), \(\mathbf{p}_{2}\), and \(\mathbf{p}_{3}\), and class \(\mathbf{s}_{2}\) is related to proxy points \(\mathbf{p}_{1}\) and \(\mathbf{p}_{4}\). The pentagrams (\(\star\star\star\)) represent proxies for each category. When considering both types of relationships, all the data points are prone to semantic bias--they will be predominantly attracted to proxy \(\mathbf{p}_{1}\) if a significantly larger proportion of them are related to proxy \(\mathbf{p}_{1}\) compared to other proxies. Unfortunately, ensuring class balance in real-world applications is challenging, which makes semantic bias a significant obstacle to the practical deployment of this approach. Worse still, despite preserving inter-class similarity relationships effectively, directly combining \(\mathcal{L}_{pair}\) and \(\mathcal{L}_{pxy}\) will cause an intra-class dispersion issue again. Considering the relationships between data point A and other data points, as well as the relationships between data point A and relevant category proxies, the connections of data point A with other data points are far more numerous than its connections with relevant category proxies.