Hashing for Similarity Search: A Survey

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

HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

Fast Cross-Polytope Locality-Sensitive Hashing

We provide a variant of cross-polytope locality sensitive hashing with respect to angular distance which is provably optimal in asymptotic sensitivity and enjoys $\mathcal{O}(d \ln d )$ hash computation time. Building on a recent result (by Andoni, Indyk, Laarhoven, Razenshteyn, Schmidt, 2015), we show that optimal asymptotic sensitivity for cross-polytope LSH is retained even when the dense Gaussian matrix is replaced by a fast Johnson-Lindenstrauss transform followed by discrete pseudo-rotation, reducing the hash computation time from $\mathcal{O}(d^2)$ to $\mathcal{O}(d \ln d )$. Moreover, our scheme achieves the optimal rate of convergence for sensitivity. By incorporating a low-randomness Johnson-Lindenstrauss transform, our scheme can be modified to require only $\mathcal{O}(\ln^9(d))$ random bitsComment: 14 pages, 6 figure

Drawbacks and Proposed Solutions for Real-time Processing on Existing State-of-the-art Locality Sensitive Hashing Techniques

Nearest-neighbor query processing is a fundamental operation for many image retrieval applications. Often, images are stored and represented by high-dimensional vectors that are generated by feature-extraction algorithms. Since tree-based index structures are shown to be ineffective for high dimensional processing due to the well-known "Curse of Dimensionality", approximate nearest neighbor techniques are used for faster query processing. Locality Sensitive Hashing (LSH) is a very popular and efficient approximate nearest neighbor technique that is known for its sublinear query processing complexity and theoretical guarantees. Nowadays, with the emergence of technology, several diverse application domains require real-time high-dimensional data storing and processing capacity. Existing LSH techniques are not suitable to handle real-time data and queries. In this paper, we discuss the challenges and drawbacks of existing LSH techniques for processing real-time high-dimensional image data. Additionally, through experimental analysis, we propose improvements for existing state-of-the-art LSH techniques for efficient processing of high-dimensional image data.Comment: Accepted and Presented at the 5th International Conference on Signal and Image Processing (SIGI-2019), Dubai, UA

Constant Sequence Extension for Fast Search Using Weighted Hamming Distance

Representing visual data using compact binary codes is attracting increasing attention as binary codes are used as direct indices into hash table(s) for fast non-exhaustive search. Recent methods show that ranking binary codes using weighted Hamming distance (WHD) rather than Hamming distance (HD) by generating query-adaptive weights for each bit can better retrieve query-related items. However, search using WHD is slower than that using HD. One main challenge is that the complexity of extending a monotone increasing sequence using WHD to probe buckets in hash table(s) for existing methods is at least proportional to the square of the sequence length, while that using HD is proportional to the sequence length. To overcome this challenge, we propose a novel fast non-exhaustive search method using WHD. The key idea is to design a constant sequence extension algorithm to perform each sequence extension in constant computational complexity and the total complexity is proportional to the sequence length, which is justified by theoretical analysis. Experimental results show that our method is faster than other WHD-based search methods. Also, compared with the HD-based non-exhaustive search method, our method has comparable efficiency but retrieves more query-related items for the dataset of up to one billion items