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79
Efficient Additive Kernels via Explicit Feature Maps
"... Maji and Berg [13] have recently introduced an explicit feature map approximating the intersection kernel. This enables efficient learning methods for linear kernels to be applied to the nonlinear intersection kernel, expanding the applicability of this model to much larger problems. In this paper ..."
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Cited by 235 (9 self)
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Maji and Berg [13] have recently introduced an explicit feature map approximating the intersection kernel. This enables efficient learning methods for linear kernels to be applied to the nonlinear intersection kernel, expanding the applicability of this model to much larger problems. In this paper we generalize this idea, and analyse a large family of additive kernels, called homogeneous, in a unified framework. The family includes the intersection, Hellinger’s, and χ2 kernels commonly employed in computer vision. Using the framework we are able to: (i) provide explicit feature maps for all homogeneous additive kernels along with closed form expression for all common kernels; (ii) derive corresponding approximate finitedimensional feature maps based on the Fourier sampling theorem; and (iii) quantify the extent of the approximation. We demonstrate that the approximations have indistinguishable performance from the full kernel on a number of standard datasets, yet greatly reduce the train/test times of SVM implementations. We show that the χ2 kernel, which has been found to yield the best performance in most applications, also has the most compact feature representation. Given these train/test advantages we are able to obtain a significant performance improvement over current state of the art results based on the intersection kernel. 1.
H (2010a) Largescale image retrieval with compressed Fisher vectors
 In: CVPR Perronnin F, Sánchez J, Liu Y (2010b) Largescale
"... The problem of largescale image search has been traditionally addressed with the bagofvisualwords (BOV). In this article, we propose to use as an alternative the Fisher kernel framework. We first show why the Fisher representation is wellsuited to the retrieval problem: it describes an image by ..."
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Cited by 104 (8 self)
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The problem of largescale image search has been traditionally addressed with the bagofvisualwords (BOV). In this article, we propose to use as an alternative the Fisher kernel framework. We first show why the Fisher representation is wellsuited to the retrieval problem: it describes an image by what makes it different from other images. One drawback of the Fisher vector is that it is highdimensional and, as opposed to the BOV, it is dense. The resulting memory and computational costs do not make Fisher vectors directly amenable to largescale retrieval. Therefore, we compress Fisher vectors to reduce their memory footprint and speedup the retrieval. We compare three binarization approaches: a simple approach devised for this representation and two standard compression techniques. We show on two publicly available datasets that compressed Fisher vectors perform very well using as little as a few hundreds of bits per image, and significantly better than a very recent compressed BOV approach. 1.
Hashing with graphs
 In ICML
, 2011
"... Hashing is becoming increasingly popular for efficient nearest neighbor search in massive databases. However, learning short codes that yield good search performance is still a challenge. Moreover, in many cases realworld data lives on a lowdimensional manifold, which should be taken into account t ..."
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Cited by 103 (30 self)
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Hashing is becoming increasingly popular for efficient nearest neighbor search in massive databases. However, learning short codes that yield good search performance is still a challenge. Moreover, in many cases realworld data lives on a lowdimensional manifold, which should be taken into account to capture meaningful nearest neighbors. In this paper, we propose a novel graphbased hashing method which automatically discovers the neighborhood structure inherent in the data to learn appropriate compact codes. To make such an approach computationally feasible, we utilize Anchor Graphs to obtain tractable lowrank adjacency matrices. Our formulation allows constant time hashingof a newdatapointbyextrapolatinggraphLaplacian eigenvectors to eigenfunctions. Finally, we describe a hierarchical threshold learning procedure in which each eigenfunction yields multiple bits, leading to higher search accuracy. Experimental comparison with the other stateoftheart methods on two large datasets demonstrates the efficacy of the proposed method. 1.
Robust 1Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
, 2011
"... The Compressive Sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is ..."
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Cited by 85 (28 self)
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The Compressive Sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that a large class of measurement mappings achieve this optimal bound. Second, we consider reconstruction robustness to measurement errors and noise and introduce the Binary ɛStable Embedding (BɛSE) property, which characterizes the robustness measurement process to sign changes. We show the same class of matrices that provide optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the Binary Iterative Hard Thresholding (BIHT) algorithm for signal reconstruction from 1bit measurements that offers stateoftheart performance.
LDAHash: Improved matching with smaller descriptors
, 2010
"... SIFTlike local feature descriptors are ubiquitously employed in such computer vision applications as contentbased retrieval, video analysis, copy detection, object recognition, phototourism and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometri ..."
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Cited by 79 (10 self)
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SIFTlike local feature descriptors are ubiquitously employed in such computer vision applications as contentbased retrieval, video analysis, copy detection, object recognition, phototourism and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptorsareonlyapproximatelyinvariantinpractice. Secondly, descriptors are usually highdimensional (e.g. SIFT is represented as a 128dimensional vector). In largescale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space, in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach.
Minimal Loss Hashing for Compact Binary Codes
"... We propose a method for learning similaritypreserving hash functions that map highdimensional data onto binary codes. The formulation is based on structured prediction with latent variables and a hingelike loss function. It is efficient to train for large datasets, scales well to large code lengths ..."
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Cited by 74 (3 self)
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We propose a method for learning similaritypreserving hash functions that map highdimensional data onto binary codes. The formulation is based on structured prediction with latent variables and a hingelike loss function. It is efficient to train for large datasets, scales well to large code lengths, and outperforms stateoftheart methods. 1.
Sequential Projection Learning for Hashing with Compact Codes
"... Hashing based Approximate Nearest Neighbor (ANN) search has attracted much attention due to its fast query time and drastically reduced storage. However, most of the hashing methods either use random projections or extract principal directions from the data to derive hash functions. The resulting em ..."
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Cited by 64 (14 self)
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Hashing based Approximate Nearest Neighbor (ANN) search has attracted much attention due to its fast query time and drastically reduced storage. However, most of the hashing methods either use random projections or extract principal directions from the data to derive hash functions. The resulting embedding suffers from poor discrimination when compact codes are used. In this paper, we propose a novel datadependent projection learning method such that each hash function is designed to correct the errors made by the previous one sequentially. The proposed method easily adapts to both unsupervised and semisupervised scenarios and shows significant performance gains over the stateoftheart methods on two large datasets containing up to 1 million points. 1.
Visual Modelling of
 Complex Business Processes with Trees, Overlays and DistortionBased Displays, Proc VLHCC’07, IEEE CS
"... evolution laws for thin crystalline films: ..."
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PICODES: Learning a Compact Code for NovelCategory Recognition
"... We introduce PICODES: a very compact image descriptor which nevertheless allows high performance on object category recognition. In particular, we address novelcategory recognition: the task of defining indexing structures and image representations which enable a large collection of images to be se ..."
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Cited by 34 (2 self)
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We introduce PICODES: a very compact image descriptor which nevertheless allows high performance on object category recognition. In particular, we address novelcategory recognition: the task of defining indexing structures and image representations which enable a large collection of images to be searched for an object category that was not known when the index was built. Instead, the training images defining the category are supplied at query time. We explicitly learn descriptors of a given length (from as small as 16 bytes per image) which have good objectrecognition performance. In contrast to previous work in the domain of object recognition, we do not choose an arbitrary intermediate representation, but explicitly learn short codes. In contrast to previous approaches to learn compact codes, we optimize explicitly for (an upper bound on) classification performance. Optimization directly for binary features is difficult and nonconvex, but we present an alternation scheme and convex upper bound which demonstrate excellent performance in practice. PICODES of 256 bytes match the accuracy of the current best known classifier for the Caltech256 benchmark, but they decrease the database storage size by a factor of 100 and speedup the training and testing of novel classes by orders of magnitude. 1