You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Due to the impressive learning power, deep learning has achieved a remarkable performance in supervised hash function learning. In this paper, we propose a novel asymmetric supervised deep hashing method to preserve the semantic structure among different categories and generate the binary codes simultaneously. Specifically, two asymmetric deep networks are constructed to reveal the similarity between each pair of images according to their semantic labels. The deep hash functions are then learned through two networks by minimizing the gap between the learned features and discrete codes. Furthermore, since the binary codes in the Hamming space also should keep the semantic affinity existing in the original space, another asymmetric pairwise loss is introduced to capture the similarity between the binary codes and real-value features. This asymmetric loss not only improves the retrieval performance, but also contributes to a quick convergence at the training phase. By taking advantage of the two-stream deep structures and two types of asymmetric pairwise functions, an alternating algorithm is designed to optimize the deep features and high-quality binary codes efficiently. Experimental results on three real-world datasets substantiate the effectiveness and superiority of our approach as compared with state-of-the-art.

Cited Abstract(s):
[1]: This paper proposes to learn binary hash codes within a statistical learning framework, in which an upper bound of the probability of Bayes decision errors is derived for different forms of hash functions and a rigorous proof of the convergence of the upper bound is presented. Consequently, minimizing such an upper bound leads to consistent performance improvements of existing hash code learning algorithms, regardless of whether original algorithms are unsupervised or supervised. This paper also illustrates a fast hash coding method that exploits simple binary tests to achieve orders of magnitude improvement in coding speed as compared to projection based methods.

[2]: Due to its low storage cost and fast query speed, hashing has been widely adopted for approximate nearest neighbor search in large-scale datasets. Traditional hashing methods try to learn the hash codes in an unsupervised way where the metric (Euclidean) structure of the training data is preserved. Very recently, supervised hashing methods, which try to preserve the semantic structure constructed from the semantic labels of the training points, have exhibited higher accuracy than unsupervised methods. In this paper, we propose a novel supervised hashing method, called latent factor hashing(LFH), to learn similarity-preserving binary codes based on latent factor models. An algorithm with convergence guarantee is proposed to learn the parameters of LFH. Furthermore, a linear-time variant with stochastic learning is proposed for training LFH on large-scale datasets. Experimental results on two large datasets with semantic labels show that LFH can achieve superior accuracy than state-of-the-art methods with comparable training time.

[3]: We propose a method for learning similarity-preserving hash functions that map high-dimensional data onto binary codes. The formulation is based on structured prediction with latent variables and a hinge-like loss function. It is efficient to train for large datasets, scales well to large code lengths, and outperforms state-of-the-art methods.

[4]: Recent years have witnessed the growing popularity of hashing in large-scale vision problems. It has been shown that the hashing quality could be boosted by leveraging supervised information into hash function learning. However, the existing supervised methods either lack adequate performance or often incur cumbersome model training. In this paper, we propose a novel kernel-based supervised hashing model which requires a limited amount of supervised information, i.e., similar and dissimilar data pairs, and a feasible training cost in achieving high quality hashing. The idea is to map the data to compact binary codes whose Hamming distances are minimized on similar pairs and simultaneously maximized on dissimilar pairs. Our approach is distinct from prior works by utilizing the equivalence between optimizing the code inner products and the Hamming distances. This enables us to sequentially and efficiently train the hash functions one bit at a time, yielding very short yet discriminative codes. We carry out extensive experiments on two image benchmarks with up to one million samples, demonstrating that our approach significantly outperforms the state-of-the-arts in searching both metric distance neighbors and semantically similar neighbors, with accuracy gains ranging from 13 to 46 .

[5]: Recently, learning based hashing techniques have attracted broad research interests because they can support efficient storage and retrieval for high-dimensional data such as images, videos, documents, etc. However, a major difficulty of learning to hash lies in handling the discrete constraints imposed on the pursued hash codes, which typically makes hash optimizations very challenging (NP-hard in general). In this work, we propose a new supervised hashing framework, where the learning objective is to generate the optimal binary hash codes for linear classification. By introducing an auxiliary variable, we reformulate the objective such that it can be solved substantially efficiently by employing a regularization algorithm. One of the key steps in this algorithm is to solve a regularization sub-problem associated with the NP-hard binary optimization. We show that the sub-problem admits an analytical solution via cyclic coordinate descent. As such, a high-quality discrete solution can eventually be obtained in an efficient computing manner, therefore enabling to tackle massive datasets. We evaluate the proposed approach, dubbed Supervised Discrete Hashing (SDH), on four large image datasets and demonstrate its superiority to the state-of-the-art hashing methods in large-scale image retrieval.
In contrast to unsupervised hashing methods, supervised hashing learning utilizes the label information to encourage the binary codes in the Hamming space to preserve the semantic relationship existing in the raw data. For instance, [3] introduced a hinge-like loss function to exploit the semantic information. Besides, [2] projected the raw data into a latent subspace, and the label information is embedded on this subspace to preserve the semantic structure. The Jensen Shannon Divergence is also utilized in [1] to learn the binary codes within a probabilistic framework, in which an upper bound is derived for various hash functions. Being similar to KLSH, [4] proposed a supervised hashing with kernels, in which the similar pairs are minimized while the dissimilar pairs are maximized. Consider the discrete constraint, the supervised discrete hashing (SDH) [5] was proposed to not only preserve the semantic structure, but also discretely learn the hash codes without any relaxation. However, this discrete optimization is time-consuming and unscalable. To tackle this problem, a novel method named column sample based discrete supervised hashing (COSDISH) was presented to directly obtain the binary codes from semantic information.