A General Two-Step Approach to Learning-Based Hashing
01 Dec 2013-pp 2552-2559
TL;DR: This framework decomposes the hashing learning problem into two steps: hash bit learning and hash function learning based on the learned bits, and can typically be formulated as binary quadratic problems, and the second step can be accomplished by training standard binary classifiers.
Abstract: Most existing approaches to hashing apply a single form of hash function, and an optimization process which is typically deeply coupled to this specific form. This tight coupling restricts the flexibility of the method to respond to the data, and can result in complex optimization problems that are difficult to solve. Here we propose a flexible yet simple framework that is able to accommodate different types of loss functions and hash functions. This framework allows a number of existing approaches to hashing to be placed in context, and simplifies the development of new problem-specific hashing methods. Our framework decomposes the hashing learning problem into two steps: hash bit learning and hash function learning based on the learned bits. The first step can typically be formulated as binary quadratic problems, and the second step can be accomplished by training standard binary classifiers. Both problems have been extensively studied in the literature. Our extensive experiments demonstrate that the proposed framework is effective, flexible and outperforms the state-of-the-art.
Citations
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Proceedings Article•
27 Jul 2014TL;DR: 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.
Abstract: 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.
925 citations
Cites background or methods from "A General Two-Step Approach to Lear..."
...Similar to the two-step paradigm in TSH (Lin et al. 2013), the proposed method decomposes the learning process into a hash code learning step and a hash function learning step....
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...Hence, similar to existing methods (Liu et al. 2012; Lin et al. 2013; Kulis and Darrell 2009), if in some iteration (of the outer loop) increases the value of (3), Algorithm 1 does not update H and L and continues the loop (see the IF-ELSE block in the outer loop of Algorithm 1)....
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...Note that there exist other algorithms to factorize S into HH , such as the block coordinate descent (BCD) algorithm in (Lin et al. 2013)....
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...Hence, similar to existing methods (Liu et al. 2012; Lin et al. 2013; Kulis and Darrell 2009), if in some iteration (of the...
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...To avoid this issue, one of the popular ways is decomposing the learning process into a hash code learning stage followed by a hash function learning stage (e.g., (Zhang et al. 2010; Lin et al. 2013))....
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07 Jun 2015
TL;DR: This work proposes a new supervised hashing framework, where the learning objective is to generate the optimal binary hash codes for linear classification, and introduces an auxiliary variable to reformulate the objective such that it can be solved substantially efficiently by employing a regularization algorithm.
Abstract: 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.
923 citations
Cites methods from "A General Two-Step Approach to Lear..."
...The similar idea was also adopted in [17,18,39]....
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TL;DR: In this paper, a comprehensive survey of the learning to hash algorithms is presented, categorizing them according to the manners of preserving the similarities into: pairwise similarity preserving, multi-wise similarity preservation, implicit similarity preserving and quantization, and discuss their relations.
Abstract: Nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest. Learning to hash is one of the major solutions to this problem and has been widely studied recently. In this paper, we present a comprehensive survey of the learning to hash algorithms, categorize them according to the manners of preserving the similarities into: pairwise similarity preserving, multiwise similarity preserving, implicit similarity preserving, as well as quantization, and discuss their relations. We separate quantization from pairwise similarity preserving as the objective function is very different though quantization, as we show, can be derived from preserving the pairwise similarities. In addition, we present the evaluation protocols, and the general performance analysis, and point out that the quantization algorithms perform superiorly in terms of search accuracy, search time cost, and space cost. Finally, we introduce a few emerging topics.
838 citations
Posted Content•
TL;DR: Supervised Discrete Hashing (SDH) as mentioned in this paper proposes a new supervised hashing framework, where the learning objective is to generate the optimal binary hash codes for linear classification, which can support efficient storage and retrieval for high-dimensional data such as images, videos, documents, etc.
Abstract: 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.
807 citations
Posted Content•
TL;DR: This paper presents a survey on one of the main solutions to approximate search, hashing, which has been widely studied since the pioneering work locality sensitive hashing, and divides the hashing algorithms into two main categories.
Abstract: 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.
531 citations
Cites methods from "A General Two-Step Approach to Lear..."
...The paper [77] presents a general two-step approach to learning-based hashing: learn binary embedding (codes) and then learn the hash function mapping the input item to the learnt binary codes....
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References
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Proceedings Article•
07 Sep 1999TL;DR: Experimental results indicate that the novel scheme for approximate similarity search based on hashing scales well even for a relatively large number of dimensions, and provides experimental evidence that the method gives improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition.
Abstract: The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the \curse of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50).
3,705 citations
Additional excerpts
...We compare with a few state-of-the-art hashing methods, including 6 (semi-)supervised methods: Supervised Hashing with Kernels (KSH) [8], Iterative Quantization with supervised embedding (ITQ-CCA) [3], Minimal Loss Hashing (MLH) [10], Supervised Binary Reconstructive Embeddings (BREs) [5] and its unsupervised version BRE, Supervised Self-Taught Hashing (STHs) [16] and its unsupervised version STH, Semi-supervised sequential Projection Learning Hashing(SPLH) [13], and 7 unsupervised methods: Locality-Sensitive Hashing (LSH) [2], Iterative Quantization (ITQ) [3], Anchor Graph Hashing (AGH) [9], Spectral Hashing (SPH [15]), Spherical Hashing (SPHER) [4], Multi-dimension Spectral Hashing (MDSH) [14], Kernelized Locality-Sensitive Hashing KLSH [6]....
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...The common forms of hash function include linear perceptron functions (MLH, SPLH, LSH), kernel functions (KSH, KLSH), eigenfunctions (SH, MDSH)....
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...One of the seminal approaches in this vain is Locality-Sensitive Hashing (LSH) [2], which randomly generates hash functions to approximate cosine similarity....
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...For each dataset, the bandwidth parameters of Gaussian affinity in MDSH and RBF kernel in KLSH, KSH and our method TSH is set as σ = td̄....
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TL;DR: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables, intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems.
Abstract: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems and in this case performs similarly to its predessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.
2,776 citations
Proceedings Article•
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08 Dec 2008
TL;DR: The problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard and a spectral method is obtained whose solutions are simply a subset of thresholded eigenvectors of the graph Laplacian.
Abstract: Semantic hashing[1] seeks compact binary codes of data-points so that the Hamming distance between codewords correlates with semantic similarity. In this paper, we show that the problem of finding a best code for a given dataset is closely related to the problem of graph partitioning and can be shown to be NP hard. By relaxing the original problem, we obtain a spectral method whose solutions are simply a subset of thresholded eigenvectors of the graph Laplacian. By utilizing recent results on convergence of graph Laplacian eigenvectors to the Laplace-Beltrami eigenfunctions of manifolds, we show how to efficiently calculate the code of a novel data-point. Taken together, both learning the code and applying it to a novel point are extremely simple. Our experiments show that our codes outperform the state-of-the art.
2,641 citations
TL;DR: For certain classes that are particularly prevalent in the dataset, such as people, this work is able to demonstrate a recognition performance comparable to class-specific Viola-Jones style detectors.
Abstract: With the advent of the Internet, billions of images are now freely available online and constitute a dense sampling of the visual world. Using a variety of non-parametric methods, we explore this world with the aid of a large dataset of 79,302,017 images collected from the Internet. Motivated by psychophysical results showing the remarkable tolerance of the human visual system to degradations in image resolution, the images in the dataset are stored as 32 x 32 color images. Each image is loosely labeled with one of the 75,062 non-abstract nouns in English, as listed in the Wordnet lexical database. Hence the image database gives a comprehensive coverage of all object categories and scenes. The semantic information from Wordnet can be used in conjunction with nearest-neighbor methods to perform object classification over a range of semantic levels minimizing the effects of labeling noise. For certain classes that are particularly prevalent in the dataset, such as people, we are able to demonstrate a recognition performance comparable to class-specific Viola-Jones style detectors.
1,871 citations
"A General Two-Step Approach to Lear..." refers background in this paper
...Applications in computer vision include content-based image retrieval, object recognition [12], image matching, etc....
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TL;DR: This paper addresses the problem of learning similarity-preserving binary codes for efficient similarity search in large-scale image collections by proposing a simple and efficient alternating minimization algorithm, dubbed iterative quantization (ITQ), and demonstrating an application of ITQ to learning binary attributes or "classemes" on the ImageNet data set.
Abstract: This paper addresses the problem of learning similarity-preserving binary codes for efficient similarity search in large-scale image collections. We formulate this problem in terms of finding a rotation of zero-centered data so as to minimize the quantization error of mapping this data to the vertices of a zero-centered binary hypercube, and propose a simple and efficient alternating minimization algorithm to accomplish this task. This algorithm, dubbed iterative quantization (ITQ), has connections to multiclass spectral clustering and to the orthogonal Procrustes problem, and it can be used both with unsupervised data embeddings such as PCA and supervised embeddings such as canonical correlation analysis (CCA). The resulting binary codes significantly outperform several other state-of-the-art methods. We also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to PCA or CCA. Finally, we demonstrate an application of ITQ to learning binary attributes or "classemes" on the ImageNet data set.
1,697 citations