# Discrete Semantics-Guided Asymmetric Hashing for Large-Scale Multimedia Retrieval  
[PERSON]  
1 School of Computer Science and Engineering, Central South University, Changsha 410083, China;  
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[PERSON]  
1 School of Computer Science and Engineering, Central South University, Changsha 410083, China;  
[EMAIL_ADDRESS]  
[PERSON]  
1 School of Computer Science and Engineering, Central South University, Changsha 410083, China;  
[EMAIL_ADDRESS]  
[PERSON]  
2 Network Resources Management and Trust Evaluation Key Laboratory of Hunan Province, Central South University, Changsha 410083, China 23 Big Data Institute, Central South University, Changsha 410083, China 32 Scar  
According to the learning principle, existing cross-modal hashing methods can be mainly divided into the following categories: **Unsupervised cross-modal hashing methods**[9; 10; 11; 12; 13; 14; 15]: Unsupervised hashing methods focus on discovering the intra- and inter-relations of multiple heterogeneous modalities without label information to learn the hash codes and corresponding hash functions. However, due to the lack of label information, the retrieval performance of unsupervised cross-modal hashing methods will be affected accordingly, i.e., \(\mathbf{x}\xrightarrow{f(\mathbf{x}^{\prime})}\mathbf{z}\xrightarrow{d( \mathbf{z}\varphi)}\mathbf{\hat{x}}\), where \(f(\cdot;\theta)\) can be considered as either a hash mapping function or an encoder, \(d(\mathbf{z};\varphi)\) can be regarded as a decoder. During the unsupervised learning process, the key design factor of this learning paradigm is the choice of a suitable metric that can measure the distance between \(\mathbf{x}\) and \(\mathbf{\hat{x}}\), i.e., the distance between \(\mathbf{x},\mathbf{\hat{x}}\) should be minimized: \(\min_{\varphi,\varphi}\mathbb{E}||\mathbf{x}-\mathbf{\hat{x}}||_{p}\), where typically \(p=2\). Then, the hash codes can be computed by \(sgn(\mathbf{z})\). **Supervised cross-modal hashing methods**[16; 17; 18; 19; 20; 21; 22]: Supervised hashing methods have obtained satisfactory retrieval results by using label information, and have been extensively studied, i.e., \(\mathbf{x}\xrightarrow{f(\mathbf{x}\varphi)}\mathbf{z}\xrightarrow{c( \mathbf{z})}\mathbf{L}\), where \(f(\cdot;\theta)\) denotes a hash mapping function that selects certain latent representation \(\mathbf{z}\), \(c(\cdot)\) denotes a classifier, \(\text{sgn}(\cdot)\) denotes the element-wise sign operation, \(\mathbf{L}\) denotes the labels, and \(\mathbf{B}\) denotes the learned hash codes. Then, the hash codes can be computed by \(sgn(\mathbf{z})\). Although supervised cross-modal hashing methods have achieved significant success, they still have the following limitations: (1) **Limited semantic utilization**. Converting the label matrix directly to the similarity matrix will lead to a semantic loss, resulting in a large semantic gap, especially when facing multi-label datasets. (2) **Inefficient learning strategy**. Some cross-modal hashing methods are based on symmetric learning strategies, resulting in a worse retrieval performance than asymmetric learning ones. (3) **Flawed optimization strategy**. As the optimization process of the hash codes is discrete, the existing optimization strategies are mainly based on two kinds, one is to use the relaxation-based strategy, which will lead to a large quantization error; the other is to use bit-to-bit optimization strategy, such as Discrete Cyclic Coordinate (DCC) descent [23]. Although the problem of quantization error is solved, optimizing the entire hash code requires \(k\) iterations, where \(k\) is the hash code length, thus the optimization process is very time-consuming. In order to solve the above limitations, in this paper, we proposed a novel yet simple but effective method, named Discrete Semantics-Guided Asymmetric Hashing (DSAH).