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Circulant Binary Embedding
"... Binary embedding of highdimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (C ..."
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Binary embedding of highdimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) which generates binary codes by projecting the data with a circulant matrix. The circulant structure enables the use of Fast Fourier Transformation to speed up the computation. Compared to methods that use unstructured matrices, the proposed method improves the time complexity from O(d2) to O(d log d), and the space complexity from O(d2) to O(d) where d is the input dimensionality. We also propose a novel timefrequency alternating optimization to learn datadependent circulant projections, which alternatively minimizes the objective in original and Fourier domains. We show by extensive experiments that the proposed approach gives much better performance than the stateoftheart approaches for fixed time, and provides much faster computation with no performance degradation for fixed number of bits. 1.
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.
Simultaneous feature learning and hash coding with deep neural networks
 in Proc. IEEE Conference on Computer Vision and Pattern Recognition
, 2015
"... Similaritypreserving hashing is a widelyused method for nearest neighbour search in largescale image retrieval tasks. For most existing hashing methods, an image is first encoded as a vector of handengineering visual features, followed by another separate projection or quantization step that g ..."
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Similaritypreserving hashing is a widelyused method for nearest neighbour search in largescale image retrieval tasks. For most existing hashing methods, an image is first encoded as a vector of handengineering visual features, followed by another separate projection or quantization step that generates binary codes. However, such visual feature vectors may not be optimally compatible with the coding process, thus producing suboptimal hashing codes. In this paper, we propose a deep architecture for supervised hashing, in which images are mapped into binary codes via carefully designed deep neural networks. The pipeline of the proposed deep architecture consists of three building blocks: 1) a subnetwork with a stack of convolution layers to produce the effective intermediate image features; 2) a divideandencode module to divide the intermediate image features into multiple branches, each encoded into one hash bit; and 3) a triplet ranking loss designed to characterize that one image is more similar to the second image than to the third one. Extensive evaluations on several benchmark image datasets show that the proposed simultaneous feature learning and hash coding pipeline brings substantial improvements over other stateoftheart supervised or unsupervised hashing methods. 1.
Compact Representation for Image Classification: To Choose or to Compress?
"... In large scale image classification, features such as Fisher vector or VLAD have achieved stateoftheart results. However, the combination of large number of examples and high dimensional vectors necessitates dimensionality reduction, in order to reduce its storage and CPU costs to a reasonable ..."
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In large scale image classification, features such as Fisher vector or VLAD have achieved stateoftheart results. However, the combination of large number of examples and high dimensional vectors necessitates dimensionality reduction, in order to reduce its storage and CPU costs to a reasonable range. In spite of the popularity of various feature compression methods, this paper argues that feature selection is a better choice than feature compression. We show that strong multicollinearity among feature dimensions may not exist, which undermines feature compression’s effectiveness and renders feature selection a natural choice. We also show that many dimensions are noise and throwing them away is helpful for classification. We propose a supervised mutual information (MI) based importance sorting algorithm to choose features. Combining with 1bit quantization, MI feature selection has achieved both higher accuracy and less computational cost than feature compression methods such as product quantization and BPBC. 1.
Understanding Locally Competitive Networks Rupesh Kumar Srivastava, Jonathan Masci,
"... Recently proposed neural network activation functions such as rectified linear, maxout, and local winnertakeall have allowed for faster and more effective training of deep neural architectures on large and complex datasets. The common trait among these functions is that they implement local com ..."
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Recently proposed neural network activation functions such as rectified linear, maxout, and local winnertakeall have allowed for faster and more effective training of deep neural architectures on large and complex datasets. The common trait among these functions is that they implement local competition between small groups of units within a layer, so that only part of the network is activated for any given input pattern. In this paper, we attempt to visualize and understand this selfmodularization, and suggest a unified explanation for the beneficial properties of such networks. We also show how our insights can be directly useful for efficiently performing retrieval over large datasets using neural networks. 1
Sparse Projections for HighDimensional Binary Codes
"... This paper addresses the problem of learning long binary codes from highdimensional data. We observe that two key challenges arise while learning and using long binary codes: (1) lack of an effective regularizer for the learned highdimensional mapping and (2) high computational cost for computin ..."
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This paper addresses the problem of learning long binary codes from highdimensional data. We observe that two key challenges arise while learning and using long binary codes: (1) lack of an effective regularizer for the learned highdimensional mapping and (2) high computational cost for computing long codes. In this paper, we overcome both these problems by introducing a sparsity encouraging regularizer that reduces the effective number of parameters involved in the learned projection operator. This regularizer not only reduces overfitting but, due to the sparse nature of the projection matrix, also leads to a dramatic reduction in the computational cost. To evaluate the effectiveness of our method, we analyze its performance on the problems of nearest neighbour search, image retrieval and image classification. Experiments on a number of challenging datasets show that our method leads to better accuracy than dense projections (ITQ [11] and LSH [16]) with the same code lengths, and meanwhile is over an order of magnitude faster. Furthermore, our method is also more accurate and faster than other recently proposed methods for speeding up highdimensional binary encoding. 1.
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.
Bilinear Random Projections for LocalitySensitive Binary Codes
"... Localitysensitive hashing (LSH) is a popular dataindependent indexing method for approximate similarity search, where random projections followed by quantization hash the points from the database so as to ensure that the probability of collision is much higher for objects that are close to each ot ..."
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Localitysensitive hashing (LSH) is a popular dataindependent indexing method for approximate similarity search, where random projections followed by quantization hash the points 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. Most of highdimensional visual descriptors for images exhibit a natural matrix structure. When visual descriptors are represented by highdimensional feature vectors and long binary codes are assigned, a random projection matrix requires expensive complexities in both space and time. In this paper we analyze a bilinear random projection method where feature matrices are transformed to binary codes by two smaller random projection matrices. We base our theoretical analysis on extending Raginsky and Lazebnik’s result where random Fourier features are composed with random binary quantizers to form locality sensitive binary codes. To this end, we answer the following two questions: (1) whether a bilinear random projection also yields similaritypreserving binary codes; (2) whether a bilinear random projection yields performance gain or loss, compared to a large linear projection. Regarding the first question, we present upper and lower bounds on the expected Hamming distance between binary codes produced by bilinear random projections. In regards to the second question, we analyze the upper and lower bounds on covariance between two bits of binary codes, showing that the correlation between two bits is small. Numerical experiments on MNIST and Flickr45K datasets confirm the validity of our method. 1.