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Supervised discrete hashing
 In Proc. CVPR
, 2015
"... Recently, learning based hashing techniques have attracted broad research interests because they can support efficient storage and retrieval for highdimensional data such as images, videos, documents, etc. However, a major difficulty of learning to hash lies in handling the discrete constraints ..."
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Recently, learning based hashing techniques have attracted broad research interests because they can support efficient storage and retrieval for highdimensional 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 (NPhard 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 subproblem associated with the NPhard binary optimization. We show that the subproblem admits an analytical solution via cyclic coordinate descent. As such, a highquality 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 stateoftheart hashing methods in largescale image retrieval. 1.
Hashing with Binary Autoencoders
"... Introduction. We consider the problem of binary hashing, where given a highdimensional vector x ∈ RD, we want to map it to an Lbit vector z = h(x) ∈ {0, 1}L using a hash function h, while preserving the neighbors of x in the binary space. Binary hashing has emerged in recent years as an effective ..."
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Introduction. We consider the problem of binary hashing, where given a highdimensional vector x ∈ RD, we want to map it to an Lbit vector z = h(x) ∈ {0, 1}L using a hash function h, while preserving the neighbors of x in the binary space. Binary hashing has emerged in recent years as an effective technique for fast search on image (and other) databases. While the search in the original space would cost O(ND) in both time and space, using floating point operations, the search in the
Hashing for Similarity Search: A Survey
, 2014
"... Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this pap ..."
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Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this paper, we present a survey on one of the main solutions, hashing, which has been widely studied since the pioneering work locality sensitive hashing. We divide the hashing algorithms two main categories: locality sensitive hashing, which designs hash functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance measure and search scheme in the hash coding space.
Optimizing AffinityBased Binary Hashing Using Auxiliary Coordinates
"... Abstract In supervised binary hashing, one wants to learn a function that maps a highdimensional feature vector to a vector of binary codes, for application to fast image retrieval. This typically results in a difficult optimization problem, nonconvex and nonsmooth, because of the discrete variable ..."
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Abstract In supervised binary hashing, one wants to learn a function that maps a highdimensional feature vector to a vector of binary codes, for application to fast image retrieval. This typically results in a difficult optimization problem, nonconvex and nonsmooth, because of the discrete variables involved. Much work has simply relaxed the problem during training, solving a continuous optimization, and truncating the codes a posteriori. This gives reasonable results but is quite suboptimal. Recent work has tried to optimize the objective directly over the binary codes and achieved better results, but the hash function was still learned a posteriori, which remains suboptimal. We propose a general framework for learning hash functions using affinitybased loss functions that uses auxiliary coordinates. This closes the loop and optimizes jointly over the hash functions and the binary codes so that they gradually match each other. The resulting algorithm can be seen as an iterated version of the procedure of optimizing first over the codes and then learning the hash function. Compared to this, our optimization is guaranteed to obtain better hash functions while being not much slower, as demonstrated experimentally in various supervised datasets. In addition, our framework facilitates the design of optimization algorithms for arbitrary types of loss and hash functions. Information retrieval arises in several applications, most obviously web search. For example, in image retrieval, a user is interested in finding similar images to a query image. Computationally, this essentially involves defining a highdimensional feature space where each relevant image is represented by a vector, and then finding the closest points (nearest neighbors) to the vector for the query image, according to a suitable distance. For example, one can use features such as SIFT or GIST [23] and the Euclidean distance for this purpose. Finding nearest neighbors in a dataset of N images (where N can be millions), each a vector of dimension D (typically in the hundreds) is slow, since exact algorithms run essentially in time O(N D) and space O(N D) (to store the image dataset). In practice, this is approximated, and a successful way to do this is binary hashing The disadvantage is that the results are inexact, since the neighbors in the binary space will not be identical to the neighbors in the original space. However, the approximation error can be controlled by using sufficiently many bits and by learning a good hash function. This has been the topic of much work in recent years. The general approach consists of defining a supervised objective that has a small value for good hash functions and minimizing it. Ideally, such an objective function should be minimal when the neighbors of any given image are the same in both original and binary spaces. Practically, in information retrieval, this is often evaluated using precision and recall. However, this 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain.
Nontransitive Hashing with Latent Similarity Components
"... Approximating the semantic similarity between entities in the learned Hamming space is the key for supervised hashing techniques. The semantic similarities between entities are often nontransitive since they could share different latent similarity components. For example, in social networks, we c ..."
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Approximating the semantic similarity between entities in the learned Hamming space is the key for supervised hashing techniques. The semantic similarities between entities are often nontransitive since they could share different latent similarity components. For example, in social networks, we connect with people for various reasons, such as sharing common interests, working in the same company, being alumni and so on. Obviously, these social connections are nontransitive if people are connected due to different reasons. However, existing supervised hashing methods treat the pairwise similarity relationships in a simple and unified way and project data into a single Hamming space, while neglecting that the nontransitive property cannot be adequately captured by a single Hamming space. In this pa
Optimizing Ranking Measures for Compact Binary Code Learning
"... Abstract. Hashing has proven a valuable tool for largescale information retrieval. Despite much success, existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest ..."
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Abstract. Hashing has proven a valuable tool for largescale information retrieval. Despite much success, existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest—multivariate performance measures such as the AUC and NDCG. Here we present a general framework (termed StructHash) that allows one to directly optimize multivariate performance measures. The resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. To solve the StructHash optimization problem, we use a combination of column generation and cuttingplane techniques. We demonstrate the generality of StructHash by applying it to ranking prediction and image retrieval, and show that it outperforms a few stateoftheart hashing methods. 1
An Ensemble Diversity Approach to Supervised Binary Hashing
"... Abstract Binary hashing is a wellknown approach for fast approximate nearestneighbor search in information retrieval. Much work has focused on affinitybased objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data po ..."
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Abstract Binary hashing is a wellknown approach for fast approximate nearestneighbor search in information retrieval. Much work has focused on affinitybased objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization. We propose a much simpler approach: we train each hash function (or bit) independently from each other, but introduce diversity among them using techniques from classifier ensembles. Surprisingly, we find that not only is this faster and trivially parallelizable, but it also improves over the more complex, coupled objective function, and achieves stateoftheart precision and recall in experiments with image retrieval. Information retrieval tasks such as searching for a query image or document in a database are essentially a nearestneighbor search Constructing hash functions that do well in retrieval measures such as precision and recall is usually done by optimizing an affinitybased objective function that relates Hamming distances to supervised neighborhood information in a training set. Many such objective functions have the form of a sum of pairwise terms that indicate whether the training points x n and x m are neighbors: Here, X = (x 1 , . . . , x N ) is the dataset of highdimensional feature vectors (e.g., SIFT features of an image), h: R D → {−1, +1} b are b binary hash functions and z = h(x) is the bbit code vector for input x ∈ R D , min h means minimizing over the parameters of the hash function h (e.g. over the weights of a linear SVM), and L(·) is a loss function that compares the codes for two images (often through their Hamming distance z n − z m ) with the groundtruth value y nm that measures the affinity in the original space between the two images x n and x m (distance, similarity or other measure of neighborhood). The sum is often restricted to a subset of image pairs (n, m) (for example, within the k nearest neighbors of each other in the original space), to keep the runtime low. The output of the algorithm is the hash function h and the binary codes Z = (z 1 , . . . , z N ) for the training points, where z n = h(x n ) for n = 1, . . . , N . Examples of these objective functions are Supervised Hashing with Kernels (KSH)
Supervised Quantization for Similarity Search
"... Abstract In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly transforms the database points into a lowdimensional ..."
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Abstract In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly transforms the database points into a lowdimensional discriminative subspace, and quantizes the data points in the transformed space. The optimization criterion is that the quantized points not only approximate the transformed points accurately, but also are semantically separable: the points belonging to a class lie in a cluster that is not overlapped with other clusters corresponding to other classes, which is formulated as a classification problem. The experiments on several standard datasets show the superiority of our approach over the stateofthe art supervised hashing and unsupervised quantization algorithms.