Visual instance search involves retrieving from a collection of images the ones that contain an instance of a visual query. Systems designed for visual instance search face the major challenge of scalability: a collection of a few million images used for instance search typically creates a few billion features that must be indexed. Furthermore, as real image collections grow rapidly, systems must also provide dynamicity, i.e., be able to handle on-line insertions while concurrently serving retrieval operations. Durability, which is the ability to recover correctly from software and hardware crashes, is the natural complement of dynamicity. Durability, however, has rarely been integrated within scalable and dynamic high-dimensional indexing solutions. This article addresses the issue of dynamicity and durability for scalable indexing of very large and rapidly growing collections of local features for instance retrieval. By extending the NV-tree, a scalable disk-based high-dimensional index, we show how to implement the ACID properties of transactions which ensure both dynamicity and durability. We present a detailed performance evaluation of the transactional NV-tree: (i) We show that the insertion throughput is excellent despite the overhead for enforcing the ACID properties; (ii) We also show that this transactional index is truly scalable using a standard image benchmark embedded in collections of up to 28.5 billion high-dimensional vectors; the largest single-server evaluations reported in the literature.
A second line of work developed around the idea of hashing. The earliest notable hashing-based method proposed was Locality Sensitive Hashing (LSH) @cite_7 @cite_21 . Essentially, LSH uses a large number of hashing functions to project high-dimensional vectors onto segmented random lines. At query time, the hash tables are probed with the query vector, and candidates from all these hash tables are then aggregated to find the true neighbors. The performance of such hashing schemes is highly dependent on the quality of the hashing functions. Hence, many approaches have been proposed to improve hashing @cite_64 @cite_26 @cite_50 @cite_38 @cite_6 @cite_29 @cite_42 , as well as to reduce the number of hash tables, which in turn diminishes the high storage costs of these tables @cite_36 @cite_40 . Tuning hash functions is reported to be a complicated task and some schemes try to automatically adapt to the data distribution @cite_10 .
@cite_38 @cite_64 @cite_26 @cite_7 @cite_36 @cite_29 @cite_21 @cite_42 @cite_6 @cite_40 @cite_50 @cite_10
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Large scale image search has recently attracted considerable attention due to easy availability of huge amounts of data. Several hashing methods have been proposed to allow approximate but highly efficient search. Unsupervised hashing methods show good performance with metric distances but, in image search, semantic similarity is usually given in terms of labeled pairs of images. There exist supervised hashing methods that can handle such semantic similarity but they are prone to overfitting when labeled data is small or noisy. Moreover, these methods are usually very slow to train. In this work, we propose a semi-supervised hashing method that is formulated as minimizing empirical error on the labeled data while maximizing variance and independence of hash bits over the labeled and unlabeled data. The proposed method can handle both metric as well as semantic similarity. The experimental results on two large datasets (up to one million samples) demonstrate its superior performance over state-of-the-art supervised and unsupervised methods. We introduce a method that enables scalable image search for learned metrics. Given pairwise similarity and dissimilarity constraints between some images, we learn a Mahalanobis distance function that captures the imagespsila underlying relationships well. To allow sub-linear time similarity search under the learned metric, we show how to encode the learned metric parameterization into randomized locality-sensitive hash functions. We further formulate an indirect solution that enables metric learning and hashing for vector spaces whose high dimensionality make it infeasible to learn an explicit weighting over the feature dimensions. We demonstrate the approach applied to a variety of image datasets. Our learned metrics improve accuracy relative to commonly-used metric baselines, while our hashing construction enables efficient indexing with learned distances and very large databases. 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 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). 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. 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. This chapter contains sections titled: The Locality-Sensitive Hashing Scheme Based on s-Stable Distributions, Approximate Near Neighbor, Exact Near Neighbor, LSH in Practice: E2LSH, Experimental Results Recently, hashing techniques have been widely applied to solve the approximate nearest neighbors search problem in many vision applications. Generally, these hashing approaches generate 2^c buckets, where c is the length of the hash code. A good hashing method should satisfy the following two requirements: 1) mapping the nearby data points into the same bucket or nearby (measured by the Hamming distance) buckets. 2) all the data points are evenly distributed among all the buckets. In this paper, we propose a novel algorithm named Complementary Projection Hashing (CPH) to find the optimal hashing functions which explicitly considers the above two requirements. Specifically, CPH aims at sequentially finding a series of hyper planes (hashing functions) which cross the sparse region of the data. At the same time, the data points are evenly distributed in the hyper cubes generated by these hyper planes. The experiments comparing with the state-of-the-art hashing methods demonstrate the effectiveness of the proposed method. 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. 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. 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. We consider the problem of indexing high-dimensional data for answering (approximate) similarity-search queries. Similarity indexes prove to be important in a wide variety of settings: Web search engines desire fast, parallel, main-memory-based indexes for similarity search on text data; database systems desire disk-based similarity indexes for high-dimensional data, including text and images; peer-to-peer systems desire distributed similarity indexes with low communication cost. We propose an indexing scheme called LSH Forest which is applicable in all the above contexts. Our index uses the well-known technique of locality-sensitive hashing (LSH), but improves upon previous designs by (a) eliminating the different data-dependent parameters for which LSH must be constantly hand-tuned, and (b) improving on LSH's performance guarantees for skewed data distributions while retaining the same storage and query overhead. We show how to construct this index in main memory, on disk, in parallel systems, and in peer-to-peer systems. We evaluate the design with experiments on multiple text corpora and demonstrate both the self-tuning nature and the superior performance of LSH Forest.