There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes longer than 32 bits are not being used as such, as it was thought to be ineffective. We introduce a rigorous way to build multiple hash tables on binary code substrings that enables exact k-nearest neighbor search in Hamming space. The approach is storage efficient and straightforward to implement. Theoretical analysis shows that the algorithm exhibits sub-linear run-time behavior for uniformly distributed codes. Empirical results show dramatic speedups over a linear scan baseline for datasets of up to one billion codes of 64, 128, or 256 bits.
* -0.2cm (Top) Curves show the ( @math ) number of distinct hash table indices (buckets) within a Hamming ball of radius @math , for different code lengths. With 64-bit codes there are about 1B buckets within a Hamming ball with a 7-bit radius. Hence with fewer than 1B database items, and a search radius of 7 or more, a hash table would be less efficient than linear scan. Using hash tables with 128-bit codes is prohibitive for radii larger than 6. (Bottom) This plot shows the expected search radius required for @math search as a function of @math , based on a dataset of 1B SIFT descriptors. Binary codes with 64 and 128 bits were obtained by random projections (LSH) from the SIFT descriptors @cite_28 . Standard deviation bars help show that large search radii are often required. * -0.2cm
@cite_28
2798834175 2108484928 2261895596 2272255885
Due to its computation efficiency and retrieval quality, hashing has been widely applied to approximate nearest neighbor search for large-scale image retrieval, while deep hashing further improves the retrieval quality by end-to-end representation learning and hash coding. With compact hash codes, Hamming space retrieval enables the most efficient constant-time search that returns data points within a given Hamming radius to each query, by hash table lookups instead of linear scan. However, subject to the weak capability of concentrating relevant images to be within a small Hamming ball due to mis-specified loss functions, existing deep hashing methods may underperform for Hamming space retrieval. This work presents Deep Cauchy Hashing (DCH), a novel deep hashing model that generates compact and concentrated binary hash codes to enable efficient and effective Hamming space retrieval. The main idea is to design a pairwise cross-entropy loss based on Cauchy distribution, which penalizes significantly on similar image pairs with Hamming distance larger than the given Hamming radius threshold. Comprehensive experiments demonstrate that DCH can generate highly concentrated hash codes and yield state-of-the-art Hamming space retrieval performance on three datasets, NUS-WIDE, CIFAR-10, and MS-COCO. 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. 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) 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.