A GPGPU Algorithm for c-Approximate r-Nearest Neighbor Search in High Dimensions

Nearest neighbor search is a fundamental problem in computer vision and machine learning. The straightforward solution, linear scan, is both computationally and memory intensive in large scale high-dimensional cases, hence is not preferable in practice. Therefore, there have been a lot of interests in algorithms that perform approximate nearest neighbor (ANN) search. In this paper, we propose a novel addition-based vector quantization algorithm, Asymmetric Mapping Quantization (AMQ), to efficiently conduct ANN search. Unlike existing addition-based quantization methods that suffer from handling the problem caused by the norm of database vector, we map the query vector and database vector using different mapping functions to transform the computation of L-2 distance to inner product similarity, thus do not need to evaluate the norm of database vector. Moreover, we further propose Distributed Asymmetric Mapping Quantization (DAMQ) to enable AMQ to work on very large dataset by distributed learning. Extensive experiments on approximate nearest neighbor search and image retrieval validate the merits of the proposed AMQ and DAMQ.

The great advances in deep learning enable human beings to extract the semantic information in ubiquitous unstructured data into high-dimensional vectors, leading to an urgent priority of managing vector data. Nearest neighbor (NN) query is a pivotal question in vector data management. Unfortunately, the NN query has been proved to be intrinsically hard. Researchers, thus, turn to approximate nearest neighbor (ANN) query which targets better efficiency by slightly compromising accuracy. Despite this, existing ANN methods still incur high time and space costs, which are mainly due to the high dimensionality. Specifically, in most in-memory ANN algorithms, the time cost is dominated by the time for comparing the distances among vectors. Each distance comparison operation (DCO) involves hundreds of arithmetic operations as each vector has hundreds of dimensions. Similarly, the space cost is dominated by the space for storing the vectors. Towards the goal of reducing the time and space costs, we present three methods in this thesis. First, we observe that, for a DCO, if an approximate distance can confirm that a vector is not a NN, then it can be discarded without computing exact distances. Based on this observation, we propose a method named ADSampling. For a DCO, it iteratively and incrementally samples a few dimensions and computes an approximate distance. When this distance is accurate enough to decide the result of the DCO, it terminates sampling. Second, to further improve the efficiency of DCOs, we design an efficient distance estimator. We propose a new quantization method named RaBitQ, which maps $D$-dimensional vectors into $D$-bit strings. RaBitQ provides an unbiased and asymptotically optimal estimator with good empirical accuracy. In addition, we introduce efficient implementations of RaBitQ based on bitwise operations or SIMD-based operations. Third, by extending the RaBitQ method, we develop an algorithm which compresses a floating-point vector into a $B$-bit unsigned integer vector. We prove that our algorithm is asymptotically optimal in terms of the space-accuracy trade-off.

K-d tree (k-dimensional tree) is a space partitioning data structure for organizing points in a k-dimensional space. K-d tree, or Multidimensional Binary Search Tree is a useful data structure for several applications such as searches involving a multidimensional search key (e.g., Range Search and Nearest Neighbour Search). K-d trees are a special case of binary space partitioning trees.KNN Search is a searching algorithm with complexity O(N log N) {N= no. of data points}. This search algorithm is relatively better than brute force search {Complexity= O(n*k); where k=No. of neighbours searched, N=No. of Data Points in Kd tree} for dimensions N>>2D {N=No. of Points, D=Dimensionality of Tree}.Furthermore, Parallel KNN Search is much more efficient and performs better than KNN Search, as it harnesses parallel processing capabilities of computers and thus, results in better search time.This paper tests the time performance of KNN Search and Parallel KNN Search and compares them by plotting it on a 3D graph. A more comprehensive comparison is done by use of 2D graphs for each dimension(from 2 to 20).

Nearest neighbor search algorithms have been successful in finding practically useful solutions to computationally difficult problems. In the nearest neighbor search problem, the brute force approach is often more efficient than other algorithms for high-dimensional spaces. A special case exists for objects represented as sparse vectors, where algorithms take advantage of the fact that an object has a zero value for most features. In general, since exact nearest neighbor search methods suffer from the “curse of dimensionality,” many practitioners use approximate nearest neighbor search algorithms when faced with high dimensionality or large datasets. To a reasonable degree, it is known that relying on approximate nearest neighbors leads to some error in the solutions to the underlying data mining problems the neighbors are used to solve. However, no one has attempted to quantify this error or provide practitioners with guidance in choosing appropriate search methods for their task. In this thesis, we conduct several experiments on recommender systems with a goal to find the degree to which approximate nearest neighbor algorithms are subject to these types of error propagation problems. Additionally, we provide persuasive evidence on the trade-off between search performance and analytics effectiveness. Our experimental evaluation demonstrates that a state-of-the-art approximate nearest neighbor search method (L2KNNGApprox) is not an effective solution in most cases. When tuned to achieve high search recall (80% or higher), it provides a fairly competitive recommendation performance compared to an efficient exact search method but offers no advantage in terms of efficiency (0.1x—1.5x speedup). Low search recall (<60%) leads to poor recommendation performance. Finally, medium recall values (60%—80%) lead to reasonable recommendation performance but are hard to achieve and offer only a modest gain in efficiency (1.5x—2.3x).

Private approximate nearest neighbor search for on-chain data based on locality-sensitive hashing

Many large multimedia applications require efficient processing of nearest neighbor queries. Often, multimedia data are represented as a collection of important high-dimensional feature vectors. Existing Locality Sensitive Hashing (LSH) techniques require users to find top-k similar feature vectors for each of the feature vectors that represent the query object. This leads to wasted and redundant work due to two main reasons: 1) not all feature vectors may contribute equally in finding the top-k similar multimedia objects, and 2) feature vectors are treated independently during query processing. Additionally, there is no theoretical guarantee on the returned multimedia results. In this work, we propose a practical and efficient indexing approach for finding top-k approximate nearest neighbors for multimedia data using LSH called mmLSH, which can provide theoretical guarantees on the returned multimedia results. Additionally, we present a buffer-conscious strategy to speed up the query processing. Experimental evaluation shows significant gains in performance time and accuracy for different real multimedia datasets when compared against state-of-the-art LSH techniques.

Speaker identification is one of the main tasks in speech processing. In addition to identification accuracy, large-scale applications of speaker identification give rise to another challenge: fast search in the database of speakers. In this paper, we propose a system based on i-vectors, a current approach for speaker identification, and locality sensitive hashing, an algorithm for fast nearest neighbor search in high dimensions. The connection between the two techniques is the cosine distance: on the one hand, we use the cosine distance to compare i-vectors, on the other hand, locality sensitive hashing allows us to quickly approximate the cosine distance in our retrieval procedure. We evaluate our approach on a realistic data set from YouTube with about 1,000 speakers. The results show that our algorithm is approximately one to two orders of magnitude faster than a linear search while maintaining the identification accuracy of an i-vector-based system.

Proximity graphs (PG) have gained increasing popularity as the state-of-the-art solutions to k -approximate nearest neighbor ( k -ANN) search on high-dimensional data, which serves as a fundamental function in various fields, e.g., retrieval-augmented generation. Although PG-based approaches have the best k -ANN search performance, their index construction cost is superlinear to the number of points. Such superlinear cost substantially limits their scalability in the era of big data. Hence, the goal of this paper is to accelerate the construction of PG-based methods without compromising their k -ANN search performance. To achieve this goal, two mainstream categories of PG are revisited: relative neighborhood graph (RNG) and navigable small world graph (NSWG). By revisiting their construction process, we find the issues of construction efficiency. To address these issues, we propose a new construction framework with a novel pruning strategy for edge selection, which accelerates RNG construction while keeping its k -ANN search performance. Then, we integrate this framework into NSWG construction to enhance both the construction efficiency and k -ANN search performance of NSWG. Extensive experiments are conducted to validate our construction framework for both RNG and NSWG, and that it significantly reduces the PG construction cost, achieving up to 5.6x speedup, while not compromising the k -ANN search performance.

Nearest neighbor search, a classic way of identifying similar data, can be applied to various areas, including database, machine learning, natural language processing, software engineering, etc. Secure nearest neighbor search aims to find nearest neighbors to a given query point over encrypted data without accessing data in plaintext. It provides privacy protection to datasets when nearest neighbor queries need to be operated by an untrusted party (e.g., a public server). While different solutions have been proposed to support nearest neighbor queries on encrypted data, these existing solutions still encounter critical drawbacks either in efficiency or privacy. In light of the limitations in the current literature, we propose a novel approximate nearest neighbor search solution, referred to as Sparser, by leveraging a combination of space-filling curves, perturbation, and Order-Preserving Encryption. The advantages of Sparser are twofold, strengthening privacy and improving efficiency. Specifically, Sparser pre-processes plaintext data with space-filling curves and perturbation, such that data is sparse, which mitigates leakage abuse attacks and renders stronger privacy. In addition to privacy enhancement, Sparser can efficiently find approximate nearest neighbors over encrypted data with logarithmic time. Through extensive experiments over real-world datasets, we demonstrate that Sparser can achieve strong privacy protection under leakage abuse attacks and minimize search time.

Exploiting lower bounds to accelerate approximate nearest neighbor search on high-dimensional data

Approximate nearest neighbor (ANN) search is a fundamental search in multi-dimensional databases, which has numerous real-world applications, such as image retrieval, recommendation, entity resolution, and sequence matching. Proximity graph (PG) has been the state-of-the-art index for ANN search. However, the search on existing PGs either suffers from a high time complexity or has no performance guarantee on the search result. In this paper, we propose a novel τ-monotonic graph (τ- MG) to address the limitations. The novelty of τ-MG lies in a τ-monotonic property. Based on this property, we prove that if the distance between a query q and its nearest neighbor is less than a constant τ, the search on τ-MG guarantees to find the exact nearest neighbor of q and the time complexity of the search is smaller than all existing PG-based methods. For index construction efficiency, we propose an approximate variant of τ-MG, namely τ-monotonic neighborhood graph (τ- MNG), which only requires the neighborhood of each node to be τ-monotonic. We further propose an optimization to reduce the number of distance computations in search. Our extensive experiments show that our techniques outperform all existing methods on well-known real-world datasets.

Broadcasting data with an index is an effective way to disseminate public information to a large clients. For a server, using multiple channels to provide services (e.g., location-based services) makes the broadcast cycle shorter than using one channel. Among location-based services, the k nearest neighbors (k-NN) search is an important one and finds the fc closest objects to a query point in a multi-dimensional space. This paper considers k nearest neighbors search on a broadcast R-tree in a multi-channel environment. We assume that a mobile client can only tune into a specified channel at one time instance. We study how a server generates the broadcast schedules on multiple channels and explore how a client executes the k-NN search on the broadcast. Different broadcast schedules with the client k-NN search processing makes different k-NN search protocols. The objectives of the protocols is to minimize the latency (i.e., the time elapsed between issuing and termination of the query), tuning time (i.e., the amount of time spent on listening to the channel), and the memory usage for k-NN search processing. Last, we present our experiments and the experiment results validate that our mechanisms achieve the objectives.

The Iterative Closest Point (ICP) algorithm is one of the most popular methods for geometric alignment of 3-dimensional data points. We focus on how to make it faster for 3D range scanner in intelligent vehicle. The ICP algorithm mainly consists of two parts: nearest neighbor search and estimation of transformation between two data sets. The former is the most time consuming process. Many variants of the k-d trees have been introduced to accelerate the search. This paper presents a remarkably efficient search procedure, exploiting two concepts of approximate nearest neighbor and local search. Consequently, the proposed algorithm is about 24 times faster than the standard k-d tree.

Overlap detection is a key step in de novo genome assembly pipelines based on the Overlap-Layout-Consensus (OLC) paradigm. Existing methods for overlap detection either rely on heuristic seed-and-extension strategies or locality-sensitive hashing (LSH), both of which struggle to handle repetitive genomic regions and the computational burden of large-scale datasets. Here, we present FEDRANN, a novel strategy for overlap graph construction that integrates feature extraction, dimensionality reduction (DR), and approximate nearest neighbor (ANN) search. We find the pipeline combining inverse document frequency (IDF) transformation, sparse random projection (SRP), and NNDescent enables accurate detection of overlaps across diverse datasets. We developed an efficient open-source implementation of this pipeline named Fedrann (https://github.com/jzhang-dev/fedrann). Through systematic benchmarking on real long-read sequencing data, we demonstrate that Fedrann produces overlap graphs comparable to or better than those generated by existing state-of-the-art tools, including MECAT2, minimap2, and wtdbg2, while maintaining competitive runtime. By integrating Fedrann into the Shasta assembler, we successfully reconstructed human whole genomes, achieving high assembly contiguity and quality. Despite being implemented primarily in Python, Fedrann achieves performance parity with tools written in compiled languages by leveraging C-accelerated numerical libraries and optimized batch-based matrix operations. Our results suggest that the combination of dimensionality reduction and ANN techniques offers a robust, scalable framework for accurate overlap detection in long-read assembly and broader sequence similarity search tasks.

Spatial interpolations are commonly used in geometric modeling for life science applications. In large-scale spatial interpolations, it is always needed to find a local set of data points for each interpolated point using the k Nearest Neighbor (kNN) search procedure. To improve the computational efficiency of kNN search, spatial decomposition structures such as grids and trees are employed to fastly locate the nearest neighbors. Among those spatial decomposition structures, the uniform grid is the simplest one, and the size of the grid cell could strongly affect the efficiency of kNN search. In this paper, we evaluate the effect of the size of uniform grid cell on the efficiency of kNN search. Our objective is to find the relatively optimal size of grid cell by considering the distribution of scattered points (i.e., the data points and the interpolated points). We employ the Standard Deviation of points’ coordinates to measure the spatial distribution of scattered points. For the irregularly distributed scattered points, we perform several series of kNN search procedures in two dimensions. Benchmark results indicate that: in two dimensions, with the increase of the Standard Deviation of points’ coordinates, the relatively optimal size of the grid cell decreases and eventually converges. The relationships between the Standard Deviation of scattered points’ coordinates and the relatively optimal size of grid cell are also fitted. The fitted relationships could be applied to determine the relatively optimal grid cell in kNN search, and further, improve the computational efficiency of spatial interpolations.