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:
In this paper, we propose training very deep neural networks (DNNs) for supervised learning of hash codes. Existing methods in this context train relatively "shallow" networks limited by the issues arising in back propagation (e.e. vanishing gradients) as well as computational efficiency. We propose a novel and efficient training algorithm inspired by alternating direction method of multipliers (ADMM) that overcomes some of these limitations. Our method decomposes the training process into independent layer-wise local updates through auxiliary variables. Empirically we observe that our training algorithm always converges and its computational complexity is linearly proportional to the number of edges in the networks. Empirically we manage to train DNNs with 64 hidden layers and 1024 nodes per layer for supervised hashing in about 3 hours using a single GPU. Our proposed very deep supervised hashing (VDSH) method significantly outperforms the state-of-the-art on several benchmark datasets.

Cited Abstract(s):
[1]: Extracting informative image features and learning effective approximate hashing functions are two crucial steps in image retrieval. Conventional methods often study these two steps separately, e.g., learning hash functions from a predefined hand-crafted feature space. Meanwhile, the bit lengths of output hashing codes are preset in the most previous methods, neglecting the significance level of different bits and restricting their practical flexibility. To address these issues, we propose a supervised learning framework to generate compact and bit-scalable hashing codes directly from raw images. We pose hashing learning as a problem of regularized similarity learning. In particular, we organize the training images into a batch of triplet samples, each sample containing two images with the same label and one with a different label. With these triplet samples, we maximize the margin between the matched pairs and the mismatched pairs in the Hamming space. In addition, a regularization term is introduced to enforce the adjacency consistency, i.e., images of similar appearances should have similar codes. The deep convolutional neural network is utilized to train the model in an end-to-end fashion, where discriminative image features and hash functions are simultaneously optimized. Furthermore, each bit of our hashing codes is unequally weighted, so that we can manipulate the code lengths by truncating the insignificant bits. Our framework outperforms state-of-the-arts on public benchmarks of similar image search and also achieves promising results in the application of person re-identification in surveillance. It is also shown that the generated bit-scalable hashing codes well preserve the discriminative powers with shorter code lengths.

[2]: With the rapid growth of web images, hashing has received increasing interests in large scale image retrieval. Research efforts have been devoted to learning compact binary codes that preserve semantic similarity based on labels. However, most of these hashing methods are designed to handle simple binary similarity. The complex multi-level semantic structure of images associated with multiple labels have not yet been well explored. Here we propose a deep semantic ranking based method for learning hash functions that preserve multilevel semantic similarity between multi-label images. In our approach, deep convolutional neural network is incorporated into hash functions to jointly learn feature representations and mappings from them to hash codes, which avoids the limitation of semantic representation power of hand-crafted features. Meanwhile, a ranking list that encodes the multilevel similarity information is employed to guide the learning of such deep hash functions. An effective scheme based on surrogate loss is used to solve the intractable optimization problem of nonsmooth and multivariate ranking measures involved in the learning procedure. Experimental results show the superiority of our proposed approach over several state-of-the-art hashing methods in term of ranking evaluation metrics when tested on multi-label image datasets.

[3]: Hashing seeks an embedding of high-dimensional objects into a similarity-preserving low-dimensional Hamming space such that similar objects are indexed by binary codes with small Hamming distances. A variety of hashing methods have been developed, but most of them resort to a single view (representation) of data. However, objects are often described by multiple representations. For instance, images are described by a few different visual descriptors (such as SIFT, GIST, and HOG), so it is desirable to incorporate multiple representations into hashing, leading to multi-view hashing. In this paper we present a deep network for multi-view hashing, referred to as deep multi-view hashing, where each layer of hidden nodes is composed of view-specific and shared hidden nodes, in order to learn individual and shared hidden spaces from multiple views of data. Numerical experiments on image datasets demonstrate the useful behavior of our deep multi-view hashing (DMVH), compared to recently-proposed multi-modal deep network as well as existing shallow models of hashing.

[4]: In this paper, we propose a new deep hashing (DH) approach to learn compact binary codes for large scale visual search. Unlike most existing binary codes learning methods which seek a single linear projection to map each sample into a binary vector, we develop a deep neural network to seek multiple hierarchical non-linear transformations to learn these binary codes, so that the nonlinear relationship of samples can be well exploited. Our model is learned under three constraints at the top layer of the deep network: 1) the loss between the original real-valued feature descriptor and the learned binary vector is minimized, 2) the binary codes distribute evenly on each bit, and 3) different bits are as independent as possible. To further improve the discriminative power of the learned binary codes, we extend DH into supervised DH (SDH) by including one discriminative term into the objective function of DH which simultaneously maximizes the inter-class variations and minimizes the intra-class variations of the learned binary codes. Experimental results show the superiority of the proposed approach over the state-of-the-arts.

[5]: Hashing is a popular approximate nearest neighbor search approach for large-scale image retrieval. Supervised hashing, which incorporates similarity dissimilarity information on entity pairs to improve the quality of hashing function learning, has recently received increasing attention. However, in the existing supervised hashing methods for images, an input image is usually encoded by a vector of handcrafted visual features. Such hand-crafted feature vectors do not necessarily preserve the accurate semantic similarities of images pairs, which may often degrade the performance of hashing function learning. In this paper, we propose a supervised hashing method for image retrieval, in which we automatically learn a good image representation tailored to hashing as well as a set of hash functions. The proposed method has two stages. In the first stage, given the pairwise similarity matrix S over training images, we propose a scalable coordinate descent method to decompose S into a product of HHT where H is a matrix with each of its rows being the approximate hash code associated to a training image. In the second stage, we propose to simultaneously learn a good feature representation for the input images as well as a set of hash functions, via a deep convolutional network tailored to the learned hash codes in H and optionally the discrete class labels of the images. Extensive empirical evaluations on three benchmark datasets with different kinds of images show that the proposed method has superior performance gains over several state-of-the-art supervised and unsupervised hashing methods.
( 1 ) Supervised hashing with deep models: Learning high-level feature representations by building deep hierarchical models have shown great potential in various applications. Researchers have been adopting deep models to jointly learn image representations and hash codes from data. Kang al [3] proposed a deep multi-view hashing (DMVH) algorithm to learn hash codes with multiple data representations. Xia al [5] proposed learning image representations for supervised hashing by approximating the data affinity matrix with CNN features. Zhao al [2] proposed a Deep Semantic Ranking Hashing (DSRH) method to preserve multilevel semantic similarity between multi-label images. Erin Liong al [4] proposed a deep hashing method to explore the nonlinear relationships among data. Zhang al [1] proposed a Deep Regularized Similarity Comparison Hashing (DRSCH) method to allow the length of output bits to be scalable. Most of the works learn hash functions on top of a deep CNN architecture. In contrast, VDSH can be built from arbitrary vector representations. When CNN features are used, our method can be viewed as fine-tuning these networks for supervised hashing. Besides, the scale and depth of our DNNs are much larger than previous methods, which pose harder challenges for training.