With the prevalence of the commodity depth cameras, the new paradigm of user interfaces based on 3D motion capturing and recognition have dramatically changed the way of interactions between human and computers. Human action recognition, as one of the key components in these devices, plays an important role to guarantee the quality of user experience. Although the model-driven methods have achieved huge success, they cannot provide a scalable solution for efficiently storing, retrieving and recognizing actions in the large-scale applications. These models are also vulnerable to the temporal translation and warping, as well as the variations in motion scales and execution rates. To address these challenges, we propose to treat the 3D human action recognition as a video-level hashing problem and propose a novel First-Take-All (FTA) Hashing algorithm capable of hashing the entire video into hash codes of fixed length. We demonstrate that this FTA algorithm produces a compact representation of the video invariant to the above mentioned variations, through which action recognition can be solved by an efficient nearest neighbor search by the Hamming distance between the FTA hash codes. Experiments on the public 3D human action datasets shows that the FTA algorithm can reach a recognition accuracy higher than 80 , with about 15 bits per frame considering there are 65 frames per video over the datasets.
The space-partitioning methods, such as Locality Sensitive Hashing (LSH) @cite_10 and Compressed Hashing @cite_6 normally partition the whole feature space into a sequence of half spaces and quantize the original features into binary bits by these half spaces. In order to preserve the Euclidean distances between high dimensional vectors with sufficient precision, long codes are usually required for these methods. To overcome this drawback, Multi-Probe LSH @cite_18 and entropy-based LSH @cite_33 are proposed to reduce the storage burden at the cost of increasing the query time. On the other hand, different paradigms of hashing algorithms have been developed to approximate distance metrics other than the Euclidean distance, such as the @math -norm distance @cite_32 and the Mahalanobis distance @cite_30 . Spherical LSH @cite_23 works for hashing a set of points on the hypersphere of an input space. There also exist several works kernelizing the LSH approaches by considering the Reproducing Kernel Hilbert Space (RKHS) @cite_25 @cite_16 .
@cite_30 @cite_18 @cite_33 @cite_32 @cite_6 @cite_23 @cite_16 @cite_10 @cite_25
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LSH (Locality Sensitive Hashing) is one of the best known methods for solving the c-approximate nearest neighbor problem in high dimensional spaces. This paper presents a variant of the LSH algorithm, focusing on the special case of where all points in the dataset lie on the surface of the unit hypersphere in a d-dimensional Euclidean space. The LSH scheme is based on a family of hash functions that preserves locality of points. This paper points out that when all points are constrained to lie on the surface of the unit hypersphere, there exist hash functions that partition the space more efficiently than the previously proposed methods. The design of these hash functions uses randomly rotated regular polytopes and it partitions the surface of the unit hypersphere like a Voronoi diagram. Our new scheme improves the exponent ρ, the main indicator of the performance of the LSH algorithm. Similarity indices for high-dimensional data are very desirable for building content-based search systems for feature-rich data such as audio, images, videos, and other sensor data. Recently, locality sensitive hashing (LSH) and its variations have been proposed as indexing techniques for approximate similarity search. A significant drawback of these approaches is the requirement for a large number of hash tables in order to achieve good search quality. This paper proposes a new indexing scheme called multi-probe LSH that overcomes this drawback. Multi-probe LSH is built on the well-known LSH technique, but it intelligently probes multiple buckets that are likely to contain query results in a hash table. Our method is inspired by and improves upon recent theoretical work on entropy-based LSH designed to reduce the space requirement of the basic LSH method. We have implemented the multi-probe LSH method and evaluated the implementation with two different high-dimensional datasets. Our evaluation shows that the multi-probe LSH method substantially improves upon previously proposed methods in both space and time efficiency. To achieve the same search quality, multi-probe LSH has a similar time-efficiency as the basic LSH method while reducing the number of hash tables by an order of magnitude. In comparison with the entropy-based LSH method, to achieve the same search quality, multi-probe LSH uses less query time and 5 to 8 times fewer number of hash tables. Efficient high-dimensional similarity search structures are essential for building scalable content-based search systems on feature-rich multimedia data. In the last decade, Locality Sensitive Hashing (LSH) has been proposed as indexing technique for approximate similarity search. Among the most recent variations of LSH, multi-probe LSH techniques have been proved to overcome the overlinear space cost drawback of common LSH. Multi-probe LSH is built on the well-known LSH technique, but it intelligently probes multiple buckets that are likely to contain query results in a hash table. Our method is inspired by previous work on probabilistic similarity search structures and improves upon recent theoretical work on multi-probe and query adaptive LSH. Whereas these methods are based on likelihood criteria that a given bucket contains query results, we define a more reliable a posteriori model taking account some prior about the queries and the searched objects. This prior knowledge allows a better quality control of the search and a more accurate selection of the most probable buckets. We implemented a nearest neighbors search based on this paradigm and performed experiments on different real visual features datasets. We show that our a posteriori scheme outperforms other multi-probe LSH while offering a better quality control. Comparisons to the basic LSH technique show that our method allows consistent improvements both in space and time efficiency. The past decade has been marked by the (continued) explosion of diverse data content and the fast development of intelligent data analytics techniques. One problem we identified in the mid-2000s was similarity search of feature-rich data. The challenge here was achieving both high accuracy and high efficiency in high-dimensional spaces. Locality sensitive hashing (LSH), which uses certain random space partitions and hash table lookups to find approximate nearest neighbors, was a promising approach with theoretical guarantees. But LSH alone was insufficient since a large number of hash tables were required to achieve good search quality. Building on an idea of Panigrahy, our multi-probe LSH method introduced the idea of intelligent probing. Given a query object, we strategically probe its neighboring hash buckets (in a query-dependent fashion) by calculating the statistical probabilities of similar objects falling into each bucket. Such intelligent probing can significantly reduce the number of hash tables while achieving high quality. In this paper, we revisit the problem motivation, the challenges, the key design considerations of multi-probe LSH, as well as discuss recent developments in this space and some questions for further research. It is well known that high-dimensional nearest neighbor retrieval is very expensive. Dramatic performance gains are obtained using approximate search schemes, such as the popular Locality-Sensitive Hashing (LSH). Several extensions have been proposed to address the limitations of this algorithm, in particular, by choosing more appropriate hash functions to better partition the vector space. All the proposed extensions, however, rely on a structured quantizer for hashing, poorly fitting real data sets, limiting its performance in practice. In this paper, we compare several families of space hashing functions in a real setup, namely when searching for high-dimension SIFT descriptors. The comparison of random projections, lattice quantizers, k-means and hierarchical k-means reveal that unstructured quantizer significantly improves the accuracy of LSH, as it closely fits the data in the feature space. We then compare two querying mechanisms introduced in the literature with the one originally proposed in LSH, and discuss their respective merits and limitations. Nearest neighbor (NN) search in high dimensional space is an essential query in many multimedia retrieval applications. Due to the curse of dimensionality, existing index structures might perform even worse than a simple sequential scan of data when answering exact NN query. To improve the efficiency of NN search, locality sensitive hashing (LSH) and its variants have been proposed to find approximate NN. They adopt hash functions that can preserve the Euclidean distance so that similar objects have a high probability of colliding in the same bucket. Given a query object, candidate for the query result is obtained by accessing the points that are located in the same bucket. To improve the precision, each hash table is associated with m hash functions to recursively hash the data points into smaller buckets and remove the false positives. On the other hand, multiple hash tables are required to guarantee a high retrieval recall. Thus, tuning a good tradeoff between precision and recall becomes the main challenge for LSH. Recently, locality sensitive B-tree(LSB-tree) has been proposed to ensure both quality and efficiency. However, the index uses random I O access. When the multimedia database is large, it requires considerable disk I O cost to obtain an approximate ratio that works in practice. In this paper, we propose a novel index structure, named HashFile, for efficient retrieval of multimedia objects. It combines the advantages of random projection and linear scan. Unlike the LSH family in which each bucket is associated with a concatenation of m hash values, we only recursively partition the dense buckets and organize them as a tree structure. Given a query point q, the search algorithm explores the buckets near the query object in a top-down manner. The candidate buckets in each node are stored sequentially in increasing order of the hash value and can be efficiently loaded into memory for linear scan. HashFile can support both exact and approximate NN queries. Experimental results show that HashFile performs better than existing indexes both in answering both types of NN queries. Locality-sensitive hashing (LSH) has emerged as the dominant algorithmic technique for similarity search with strong performance guarantees in high-dimensional spaces. A drawback of traditional LSH schemes is that they may have , i.e., the recall is less than 100 . This limits the applicability of LSH in settings requiring precise performance guarantees. Building on the recent theoretical "CoveringLSH" construction that eliminates false negatives, we propose a fast and practical covering LSH scheme for Hamming space called . Inheriting the design benefits of CoveringLSH our method avoids false negatives and always reports all near neighbors. Compared to CoveringLSH we achieve an asymptotic improvement to the hash function computation time from @math to @math , where @math is the dimensionality of data and @math is the number of hash tables. Our experiments on synthetic and real-world data sets demonstrate that is comparable (and often superior) to traditional hashing-based approaches for search radius up to 20 in high-dimensional Hamming space. We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an @math -point data set in a @math -dimensional space our data structure achieves query time @math and space @math , where @math for the Euclidean space and approximation @math . For the Hamming space, we obtain an exponent of @math . Our result completes the direction set forth in [AINR14] who gave a proof-of-concept that data-dependent hashing can outperform classical Locality Sensitive Hashing (LSH). In contrast to [AINR14], the new bound is not only optimal, but in fact improves over the best (optimal) LSH data structures [IM98,AI06] for all approximation factors @math . From the technical perspective, we proceed by decomposing an arbitrary dataset into several subsets that are, in a certain sense, pseudo-random. Locality Sensitive Hashing (LSH) has emerged as the method of choice for high dimensional similarity search, a classical problem of interest in numerous applications. LSH-based solutions require that each data point be inserted into a number A of hash tables, after which a query can be answered by performing B lookups. The original LSH solution of [IM98] showed for the first time that both A and B can be made sublinear in the number of data points. Unfortunately, the classical LSH solution does not provide any tradeoff between insert and query complexity, whereas for data (respectively, query) intensive applications one would like to minimize insert time by choosing a smaller @math (respectively, minimize query time by choosing a smaller B). A partial remedy for this is provided by Entropy LSH [Pan06], which allows to make either inserts or queries essentially constant time at the expense of a loss in the other parameter, but no algorithm that achieves a smooth tradeoff is known. In this paper, we present an algorithm for performing similarity search under the Euclidean metric that resolves the problem above. Our solution is inspired by Entropy LSH, but uses a very different analysis to achieve a smooth tradeoff between insert and query complexity. Our results improve upon or match, up to lower order terms in the exponent, best known data-oblivious algorithms for the Euclidean metric. Locality-sensitive hashing (LSH) is the basis of many algorithms that use a probabilistic approach to find nearest neighbors. We describe an algorithm for optimizing the parameters and use of LSH. Prior work ignores these issues or suggests a search for the best parameters. We start with two histograms: one that characterizes the distributions of distances to a point's nearest neighbors and the second that characterizes the distance between a query and any point in the data set. Given a desired performance level (the chance of finding the true nearest neighbor) and a simple computational cost model, we return the LSH parameters that allow an LSH index to meet the performance goal and have the minimum computational cost. We can also use this analysis to connect LSH to deterministic nearest-neighbor algorithms such as @math - @math trees and thus start to unify the two approaches. We consider a new construction of locality-sensitive hash functions for Hamming space that is covering in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius r. The construction is efficient in the sense that the expected number of hash collisions between vectors at distance cr, for a given c > 1, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (FOCS '98). The efficiency of the new construction essentially matches their bound if cr = log(n) k, where n is the number of points in the data set and k ∈ N, and differs from it by at most a factor ln(4) in the exponent for general values of cr. As a consequence, LSH-based similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency. Locality-sensitive hashing (LSH) is a basic primitive in several large-scale data processing applications, including nearest-neighbor search, de-duplication, clustering, etc. In this paper we propose a new and simple method to speed up the widely-used Euclidean realization of LSH. At the heart of our method is a fast way to estimate the Euclidean distance between two d-dimensional vectors; this is achieved by the use of randomized Hadamard transforms in a non-linear setting. This decreases the running time of a (k, L)-parameterized LSH from O(dkL) to O(dlog d + kL). Our experiments show that using the new LSH in nearest-neighbor applications can improve their running times by significant amounts. To the best of our knowledge, this is the first running time improvement to LSH that is both provable and practical. We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions. Nearest neighbor (NN) search in high dimensional space is an important problem in many applications. Ideally, a practical solution (i) should be implementable in a relational database, and (ii) its query cost should grow sub-linearly with the dataset size, regardless of the data and query distributions. Despite the bulk of NN literature, no solution fulfills both requirements, except locality sensitive hashing (LSH). The existing LSH implementations are either rigorous or adhoc. Rigorous-LSH ensures good quality of query results, but requires expensive space and query cost. Although adhoc-LSH is more efficient, it abandons quality control, i.e., the neighbor it outputs can be arbitrarily bad. As a result, currently no method is able to ensure both quality and efficiency simultaneously in practice. Motivated by this, we propose a new access method called the locality sensitive B-tree (LSB-tree) that enables fast high-dimensional NN search with excellent quality. The combination of several LSB-trees leads to a structure called the LSB-forest that ensures the same result quality as rigorous-LSH, but reduces its space and query cost dramatically. The LSB-forest also outperforms adhoc-LSH, even though the latter has no quality guarantee. Besides its appealing theoretical properties, the LSB-tree itself also serves as an effective index that consumes linear space, and supports efficient updates. Our extensive experiments confirm that the LSB-tree is faster than (i) the state of the art of exact NN search by two orders of magnitude, and (ii) the best (linear-space) method of approximate retrieval by an order of magnitude, and at the same time, returns neighbors with much better quality. Hashing is used to learn binary-code representation for data with expectation of preserving the neighborhood structure in the original feature space. Due to its fast query speed and reduced storage cost, hashing has been widely used for efficient nearest neighbor search in a large variety of applications like text and image retrieval. Most existing hashing methods adopt Hamming distance to measure the similarity (neighborhood) between points in the hashcode space. However, one problem with Hamming distance is that it may destroy the neighborhood structure in the original feature space, which violates the essential goal of hashing. In this paper, Manhattan hashing (MH), which is based on Manhattan distance, is proposed to solve the problem of Hamming distance based hashing. The basic idea of MH is to encode each projected dimension with multiple bits of natural binary code (NBC), based on which the Manhattan distance between points in the hashcode space is calculated for nearest neighbor search. MH can effectively preserve the neighborhood structure in the data to achieve the goal of hashing. To the best of our knowledge, this is the first work to adopt Manhattan distance with NBC for hashing. Experiments on several large-scale image data sets containing up to one million points show that our MH method can significantly outperform other state-of-the-art methods. In computer vision there has been increasing interest in learning hashing codes whose Hamming distance approximates the data similarity. The hashing functions play roles in both quantizing the vector space and generating similarity-preserving codes. Most existing hashing methods use hyper-planes (or kernelized hyper-planes) to quantize and encode. In this paper, we present a hashing method adopting the k-means quantization. We propose a novel Affinity-Preserving K-means algorithm which simultaneously performs k-means clustering and learns the binary indices of the quantized cells. The distance between the cells is approximated by the Hamming distance of the cell indices. We further generalize our algorithm to a product space for learning longer codes. Experiments show our method, named as K-means Hashing (KMH), outperforms various state-of-the-art hashing encoding methods. Although Locality-Sensitive Hashing (LSH) is a promising approach to similarity search in high-dimensional spaces, it has not been considered practical partly because its search quality is sensitive to several parameters that are quite data dependent. Previous research on LSH, though obtained interesting asymptotic results, provides little guidance on how these parameters should be chosen, and tuning parameters for a given dataset remains a tedious process. To address this problem, we present a statistical performance model of Multi-probe LSH, a state-of-the-art variance of LSH. Our model can accurately predict the average search quality and latency given a small sample dataset. Apart from automatic parameter tuning with the performance model, we also use the model to devise an adaptive LSH search algorithm to determine the probing parameter dynamically for each query. The adaptive probing method addresses the problem that even though the average performance is tuned for optimal, the variance of the performance is extremely high. We experimented with three different datasets including audio, images and 3D shapes to evaluate our methods. The results show the accuracy of the proposed model: the recall errors predicted are within 5 from the real values for most cases; the adaptive search method reduces the standard deviation of recall by about 50 over the existing method. Nearest Neighbor (NN) search in high-dimensional space is an important problem in many applications. From the database perspective, a good solution needs to have two properties: (i) it can be easily incorporated in a relational database, and (ii) its query cost should increase sublinearly with the dataset size, regardless of the data and query distributions. Locality-Sensitive Hashing (LSH) is a well-known methodology fulfilling both requirements, but its current implementations either incur expensive space and query cost, or abandon its theoretical guarantee on the quality of query results. Motivated by this, we improve LSH by proposing an access method called the Locality-Sensitive B-tree (LSB-tree) to enable fast, accurate, high-dimensional NN search in relational databases. The combination of several LSB-trees forms a LSB-forest that has strong quality guarantees, but improves dramatically the efficiency of the previous LSH implementation having the same guarantees. In practice, the LSB-tree itself is also an effective index which consumes linear space, supports efficient updates, and provides accurate query results. In our experiments, the LSB-tree was faster than: (i) iDistance (a famous technique for exact NN search) by two orders of magnitude, and (ii) MedRank (a recent approximate method with nontrivial quality guarantees) by one order of magnitude, and meanwhile returned much better results. As a second step, we extend our LSB technique to solve another classic problem, called Closest Pair (CP) search, in high-dimensional space. The long-term challenge for this problem has been to achieve subquadratic running time at very high dimensionalities, which fails most of the existing solutions. We show that, using a LSB-forest, CP search can be accomplished in (worst-case) time significantly lower than the quadratic complexity, yet still ensuring very good quality. In practice, accurate answers can be found using just two LSB-trees, thus giving a substantial reduction in the space and running time. In our experiments, our technique was faster: (i) than distance browsing (a well-known method for solving the problem exactly) by several orders of magnitude, and (ii) than D-shift (an approximate approach with theoretical guarantees in low-dimensional space) by one order of magnitude, and at the same time, outputs better results. Binary hashing has been widely used for efficient similarity search due to its query and storage efficiency. In most existing binary hashing methods, the high-dimensional data are embedded into Hamming space and the distance or similarity of two points are approximated by the Hamming distance between their binary codes. The Hamming distance calculation is efficient, however, in practice, there are often lots of results sharing the same Hamming distance to a query, which makes this distance measure ambiguous and poses a critical issue for similarity search where ranking is important. In this paper, we propose a weighted Hamming distance ranking algorithm (WhRank) to rank the binary codes of hashing methods. By assigning different bit-level weights to different hash bits, the returned binary codes are ranked at a finer-grained binary code level. We give an algorithm to learn the data-adaptive and query-sensitive weight for each hash bit. Evaluations on two large-scale image data sets demonstrate the efficacy of our weighted Hamming distance for binary code ranking. Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We devise a new strategy that avoids partitioning the vector space and present a novel randomized algorithm that runs in time linear in dimensionality of the space and sub-linear in the intrinsic dimensionality and the size of the dataset and takes space constant in dimensionality of the space and linear in the size of the dataset. The proposed algorithm allows fine-grained control over accuracy and speed on a per-query basis, automatically adapts to variations in data density, supports dynamic updates to the dataset and is easy-to-implement. We show appealing theoretical properties and demonstrate empirically that the proposed algorithm outperforms locality-sensitivity hashing (LSH) in terms of approximation quality, speed and space efficiency.