Approximate Nearest Neighbor Search Research Articles

An efficient infinity norm minimization algorithm for under-determined inverse problems

The problem of solving under-determined systems of linear equations with minimum peak magnitude (ℓ∞ norm) has numerous applications in signal processing. These include Peak-to-Average Power Ratio (PAPR) reduction in MIMO-OFDM systems, vector quantization, approximate nearest neighbor search, optimal control in robotics, and power grid optimization. Several methods have been proposed to address this problem, but they often face limitations in computational speed or representation accuracy. Some methods also impose constraints on the frame matrix, such as restrictions on the type of its entries or its aspect ratio. In this paper, we present the Fast Iterative Peak Shrinkage Algorithm (FIPSA), which iterates over feasible solutions to consistently reduce peak magnitude and provably converge to near-optimal solutions. Our experimental results, conducted across various frame matrix types and aspect ratios, demonstrate that FIPSA consistently achieves near-minimal ℓ∞ norm values. In addition, it operates 1.3 to 7.3 times faster than previous methods, while maintaining an average representation error of 10−15. Notably, these advancements are achieved without imposing any constraints on the frame matrix.

In-memory search with learning to hash based on resistive memory for recommendation acceleration

Similarity search is essential in current artificial intelligence applications and widely utilized in various fields, such as recommender systems. However, the exponential growth of data poses significant challenges in search time and energy consumption on traditional digital hardware. Here, we propose a software-hardware co-optimization to address these challenges. On the software side, we employ a learning-to-hash method for vector encoding and achieve an approximate nearest neighbor search by calculating Hamming distance, thereby reducing computational complexity. On the hardware side, we leverage the resistance random-access memory crossbar array to implement the hash encoding process and the content-addressable memory with an in-memory computing paradigm to lower the energy consumption during searches. Simulations on the MovieLens dataset demonstrate that the implementation achieves comparable accuracy to software and reduces energy consumption by 30-fold compared to traditional digital systems. These results provide insight into the development of energy-efficient in-memory search systems for edge computing.

Spatial-Aware and Load Balancing Distributed Data Partitioning Strategies for Content-Based Multimedia Retrieval.

Content-Based Multimedia Retrieval (CBMR) has become very popular in several applications, driven by the growing routine use of multimedia data. Since the datasets used in real-world applications are very large and descriptor's dimensionality is high, querying is an expensive, albeit important functionality. Further, exact search is prohibitive in most cases, motivating the use of Approximate Nearest Neighbour Search (ANNS) algorithms, trading accuracy for performance. These have been mainly developed targeting a sequential execution in a single node. However, the large and increasing datasets used and the high query loads submitted to those systems typically surpass the memory and computing resources available in a single node. This motivated the development of parallel distributed memory ANNS solutions to meet the computing capabilities required by those applications. A common problem that must be handled when using distributed memory systems is data partitioning and its impact on load imbalance. Several data partitioning approaches have already been proposed, including elaborated spatial-aware strategies. However, little effort has been put into carefully analyzing the performance of those strategies at scale. Here, we evaluated the commonly used data partitioning strategies in ANNS and identified their limitations to propose a novel class of partitioning algorithms that can minimize load imbalance while improving data locality to attain high performance on the distributed memory search. Experimentally, we found that our proposed algorithms (SABBS and SABBSR) improved search performance by up to 1.64× compared to the best previous solution. In a distributed memory weak scaling evaluation, with up to 12 billion 128-dimensional descriptors and 60 compute nodes, the gains were maintained as the system scaled with our novel approaches. These results demonstrate the efficiency of our new algorithms for billion-scale ANNS and the importance of considering not only data locality but also data and load imbalance in the data partitioning.

Similarity search on social networks with incremental graph indexing based on probabilistic inference

PurposeThis paper aims to propose an incremental graph indexing method based on probabilistic inferences in Bayesian network (BN) for approximate nearest neighbor search (ANNS) that adds unindexed queries into the graph index incrementally.Design/methodology/approachThis paper first uses the attention mechanism based graph convolutional network to embed a social network into the low-dimensional vector space, which could improve the efficiency of graph index construction. To add the unindexed queries into the graph index incrementally, this study proposes to learn the rule-based BN from social interactions. Thus, the dependency relations of unindexed queries and their neighbors are represented, and the probabilistic inferences in BN are then performed.FindingsExperimental results demonstrate that the proposed method improves the search precision by at least 5% and search efficiency by 10% compared to the state-of-the-art methods.Originality/valueThis paper proposes a novel method to construct the incremental graph index based on probabilistic inferences in BN, such that both indexed and unindexed queries in ANNS could be addressed efficiently.

RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search

Searching for approximate nearest neighbors (ANN) in the high-dimensional Euclidean space is a pivotal problem. Recently, with the help of fast SIMD-based implementations, Product Quantization (PQ) and its variants can often efficiently and accurately estimate the distances between the vectors and have achieved great success in the in-memory ANN search. Despite their empirical success, we note that these methods do not have a theoretical error bound and are observed to fail disastrously on some real-world datasets. Motivated by this, we propose a new randomized quantization method named RaBitQ, which quantizes D-dimensional vectors into D-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations. Extensive experiments on real-world datasets confirm that (1) our method outperforms PQ and its variants in terms of accuracy-efficiency trade-off by a clear margin and (2) its empirical performance is well-aligned with our theoretical analysis.

DET-LSH: A Locality-Sensitive Hashing Scheme with Dynamic Encoding Tree for Approximate Nearest Neighbor Search

Locality-sensitive hashing (LSH) is a well-known solution for approximate nearest neighbor (ANN) search in high-dimensional spaces due to its robust theoretical guarantee on query accuracy. Traditional LSH-based methods mainly focus on improving the efficiency and accuracy of the query phase by designing different query strategies, but pay little attention to improving the efficiency of the indexing phase. They typically fine-tune existing data-oriented partitioning trees to index data points and support their query strategies. However, their strategy to directly partition the multi-dimensional space is time-consuming, and performance degrades as the space dimensionality increases. In this paper, we design an encoding-based tree called Dynamic Encoding Tree (DE-Tree) to improve the indexing efficiency and support efficient range queries based on Euclidean distance. Based on DE-Tree, we propose a novel LSH scheme called DET-LSH. DET-LSH adopts a novel query strategy, which performs range queries in multiple independent index DE-Trees to reduce the probability of missing exact NN points, thereby improving the query accuracy. Our theoretical studies show that DET-LSH enjoys probabilistic guarantees on query accuracy. Extensive experiments on real-world datasets demonstrate the superiority of DET-LSH over the state-of-the-art LSH-based methods on both efficiency and accuracy. While achieving better query accuracy than competitors, DET-LSH achieves up to 6x speedup in indexing time and 2x speedup in query time over the state-of-the-art LSH-based methods.

Terminal Embeddings in Sublinear Time

Recently (Elkin, Filtser, Neiman 2017) introduced the concept of a {\it terminal embedding} from one metric space $(X,d_X)$ to another $(Y,d_Y)$ with a set of designated terminals $T\subset X$. Such an embedding $f$ is said to have distortion $\rho\ge 1$ if $\rho$ is the smallest value such that there exists a constant $C>0$ satisfying \begin{equation*} \forall x\in T\ \forall q\in X,\ C d_X(x, q) \le d_Y(f(x), f(q)) \le C \rho d_X(x, q) . \end{equation*} When $X,Y$ are both Euclidean metrics with $Y$ being $m$-dimensional, recently (Narayanan, Nelson 2019), following work of (Mahabadi, Makarychev, Makarychev, Razenshteyn 2018), showed that distortion $1+\epsilon$ is achievable via such a terminal embedding with $m = O(\epsilon^{-2}\log n)$ for $n := |T|$. This generalizes the Johnson-Lindenstrauss lemma, which only preserves distances within $T$ and not to $T$ from the rest of space. The downside of prior work is that evaluating their embedding on some $q\in \mathbb{R}^d$ required solving a semidefinite program with $\Theta(n)$ constraints in~$m$ variables and thus required some superlinear $\mathrm{poly}(n)$ runtime. Our main contribution in this work is to give a new data structure for computing terminal embeddings. We show how to pre-process $T$ to obtain an almost linear-space data structure that supports computing the terminal embedding image of any $q\in\mathbb{R}^d$ in sublinear time $O^* (n^{1-\Theta(\epsilon^2)} + d)$. To accomplish this, we leverage tools developed in the context of approximate nearest neighbor search.

SeRF: Segment Graph for Range-Filtering Approximate Nearest Neighbor Search

Effective vector representation models, e.g., word2vec and node2vec, embed real-world objects such as images and documents in high dimensional vector space. In the meanwhile, the objects are often associated with attributes such as timestamps and prices. Many scenarios need to jointly query the vector representations of the objects together with their attributes. These queries can be formalized as range-filtering approximate nearest neighbor search (ANNS) queries. Specifically, given a collection of data vectors, each associated with an attribute value whose domain has a total order. The range-filtering ANNS consists of a query range and a query vector. It finds the approximate nearest neighbors of the query vector among all the data vectors whose attribute values fall in the query range. Existing approaches suffer from a rapidly degrading query performance when the query range width shifts. The query performance can be optimized by a solution that builds an ANNS index for every possible query range; however, the index time and index size become prohibitive -- the number of query ranges is quadratic to the number n of data vectors. To overcome these challenges, for the query range contains all attribute values smaller than a user-provided threshold, we design a structure called the segment graph whose index time and size are the same as a single ANNS index, yet can losslessly compress the n ANNS indexes, reducing the indexing cost by a factor of Ω(n). To handle general range queries, we propose a 2D segment graph with average-case index size O(n log n) to compress n segment graphs, breaking the quadratic barrier. Extensive experiments conducted on real-world datasets show that our proposed structures outperformed existing methods significantly; our index also exhibits superior scalability.

ANNProof: Building a verifiable and efficient outsourced approximate nearest neighbor search system on blockchain

Data-as-a-service is increasingly prevalent, with outsourced K-approximate nearest neighbors search (K-ANNS) gaining popularity in applications like similar image retrieval and anti-money laundering. However, malicious search service providers and dataset providers in current outsourced query systems cause incorrect user query results. To address this, we propose ANNProof, a novel framework supporting verifiable outsourced K-ANNS on the blockchain. ANNProof utilizes two innovative authenticated data structures (ADS), the Merkle HNSW node tree, and the Merkle vector identifier tree, for efficient K-ANNS query verification. Additionally, we employ the Merkle sharding tree as an ADS optimization technique, reducing the overhead of delivering verifiable queries. We implement the ADS construction protocol based on blockchain smart contracts to ensure tamper-evident datasets and enhance execution efficiency via a contract state consistency checking scheme. Extensive evaluations show that ANNProof reduces VO generation time, result verification time, and VO size by 160, 120, and 28×, respectively, compared to the state-of-the-art systems. Moreover, ADS construction using ANNProof takes at most 2% of the index construction time, resulting in a negligible overhead for implementing verifiable queries. Meanwhile, the sharding optimization accelerates ADS updates by 53×.

Bridging Software-Hardware for CXL Memory Disaggregation in Billion-Scale Nearest Neighbor Search

We propose CXL-ANNS , a software-hardware collaborative approach to enable scalable approximate nearest neighbor search (ANNS) services. To this end, we first disaggregate DRAM from the host via compute express link (CXL) and place all essential datasets into its memory pool. While this CXL memory pool allows ANNS to handle billion-point graphs without an accuracy loss, we observe that the search performance significantly degrades because of CXL’s far-memory-like characteristics. To address this, CXL-ANNS considers the node-level relationship and caches the neighbors in local memory, which are expected to visit most frequently. For the uncached nodes, CXL-ANNS prefetches a set of nodes most likely to visit soon by understanding the graph traversing behaviors of ANNS. CXL-ANNS is also aware of the architectural structures of the CXL interconnect network and lets different hardware components collaborate with each other for the search. Furthermore, it relaxes the execution dependency of neighbor search tasks and allows ANNS to utilize all hardware in the CXL network in parallel. Our evaluation shows that CXL-ANNS exhibits 93.3% lower query latency than state-of-the-art ANNS platforms that we tested. CXL-ANNS also outperforms an oracle ANNS system that has unlimited local DRAM capacity by 68.0%, in terms of latency.

Learning Adaptive Hypersphere: Boosting Efficiency on Approximate Nearest Neighbor Search

Learning Adaptive Hypersphere: Boosting Efficiency on Approximate Nearest Neighbor Search

Chunk2vec: A novel resemblance detection scheme based on Sentence‐BERT for post‐deduplication delta compression in network transmission

AbstractDelta compression, as a complementary technique for data deduplication, has gained widespread attention in network storage systems. It can eliminate redundant data between non‐duplicate but similar chunks that cannot be identified by data deduplication. The network transmission overhead between servers and clients can be greatly reduced by using data deduplication and delta compression techniques. Resemblance detection is a technique that identifies similar chunks for post‐deduplication delta compression in network storage systems. The existing resemblance detection approaches fail to detect similar chunks with arbitrary similarity by setting a similarity threshold, which can be suboptimal. In this paper, the authors propose Chunk2vec, a resemblance detection scheme for delta compression that utilizes deep learning techniques and Approximate Nearest Neighbour Search technique to detect similar chunks with any given similarity range. Chunk2vec uses a deep neural network, Sentence‐BERT, to extract an approximate feature vector for each chunk while preserving its similarity with other chunks. The experimental results on five real‐world datasets indicate that Chunk2vec improves the accuracy of resemblance detection for delta compression and achieves higher compression ratio than the state‐of‐the‐art resemblance detection technique.

Deep Learning to Hash with Application to Cross-View Nearest Neighbor Search

Learning hash functions for approximate nearest neighbor search of high-dimensional data has received a surge of interests in recent years. Most existing methods are often concerned with learning hash functions for nearest neighbor search on high-dimensional data from a single source. In many real-world applications, data can be collected from diverse sources or represented using different feature descriptors. This raises an open challenge, i.e., the Cross-View Nearest Neighbor Search (CVNNS), where the representation of a query instance can be different from that of target instances to be retrieved in database. The key challenge of cross-view search is to learn an effective shared representation which can effectively connect the query instance and the target instances to be retrieved. In this paper, we present a new cross-view nearest neighbor search scheme by applying the emerging deep learning to hash techniques. In particular, we investigate two different architectures of deep Restricted Boltzmann Machines (RBMs) for learning to hash toward cross-view nearest neighbor search, and conduct extensive experiments to examine their empirical performance on diverse settings of cross-view image retrieval tasks. The encouraging results show that our technique outperforms the state-of-the-art approaches.

Multi-label contrastive hashing

Joint learning of image representation and hash encoding represents a dominant solution to approximate nearest neighbor search for large-scale image retrieval. Despite significant advances in deep learning to hash in multi-label setting, optimization of semantic similarity-preserving representations with minimal quantization error remains challenging. Motivated by the recent success of contrastive representation learning in various vision tasks, this article introduces a Multi-label Contrastive Hashing (MCH) method for large-scale multi-label image retrieval. We extend the image similarity modeling in existing supervised contrastive loss from binary to multi-level structure, by which multi-level semantic similarity between multi-label images can be well modeled and captured in learning to hash. Despite the appealing properties of contrastive learning, directly adapting it into multi-label hashing is non-trivial, as the quantization loss may restricts the optimization of the multi-level contrastive loss, degrading the multi-level similarity-preserving hashing. To this end, we design a curriculum strategy to adaptively adjust the weight of quantization loss by leveraging the historical quantization deviations during training, such that the multi-level semantic similarity can be well preserved with progressively reduced quantization deviation. We conduct extensive experiments on three benchmark datasets including MirFlickr25k, NUS-WIDE, and IAPRTC-12. The results indicate the effectiveness of our approach, outperforming several state-of-the-art solutions for hashing-based multi-label image retrieval.

Semi-supervised inverted file index approach for approximate nearest neighbor search

This paper introduces a novel modification to the Inverted File (IVF) index approach for approximate nearest neighbor search, incorporating supervised learning techniques to enhance the efficacy of intermediate clustering and achieve more balanced cluster sizes. The proposed method involves creating clusters using a neural network by solving a task to classify query vectors into the same bucket as their corresponding nearest neighbor vectors in the original dataset. When combined with minimizing the standard deviation of the bucket sizes, the indexing process becomes more efficient and accurate during the approximate nearest neighbor search. Through empirical evaluation on a test dataset, we demonstrate that the proposed semi-supervised IVF index approach outperforms the industry-standard IVF implementation with fixed parameters, including the total number of clusters and the number of clusters allocated to queries. This novel approach has promising implications for enhancing nearest-neighbor search efficiency in high-dimensional datasets across various applications, including information retrieval, natural language search, recommendation systems, etc.

Flexible product quantization for fast approximate nearest neighbor search

Flexible product quantization for fast approximate nearest neighbor search

Deep Learning for Approximate Nearest Neighbour Search: A Survey and Future Directions

Approximate nearest neighbour search (ANNS) in high-dimensional space is an essential and fundamental operation in many applications from many domains such as multimedia database, information retrieval and computer vision. With the rapidly growing volume of data and the dramatically increasing demands of users, traditional heuristic-based ANNS solutions have been facing great challenges in terms of both efficiency and accuracy. Inspired by the recent successes of deep learning in many fields, substantial efforts have been devoted to applying deep learning techniques to ANNS for learning to index and learning to search, resulting in numerous algorithms that achieve state-of-the-art performance compared with conventional methods. In this survey paper, we comprehensively review the different types of deep learning-based ANNS methods according to two learning paradigms: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">learning to index</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">learning to search</i> . We provide a comprehensive overview and analysis of these methods in a systematic manner. Based on the overview, we point out that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">end-to-end learning</i> will be a new and promising research direction for deep learning-based ANNS, i.e., applying deep learning techniques to jointly learn the indexing and searching together, such that the underlying knowledge learned from data can directly contribute to the final searching performance. Finally, we conduct experiments and provide general performance analyses for the representative deep learning-based ANNS algorithms.

Quantization to speedup approximate nearest neighbor search

The quantization-based approaches not only are the effective methods for solving the problems of approximate nearest neighbor search, but also effectively reduce storage space. However, many quantization-based approaches usually employ fixed nprobes to the search process for each query. This will lead to extra query consumption. Additionally, we observed that as the number of points in each cluster center of product quantization increases, the query cost also increases. To address this issue, we propose an acceleration strategy based on the IVF-HNSW framework to further speed up the query process. This strategy involves introducing an adaptive termination condition for queries and reducing the number of data points accessed by building HNSW results. Through extensive experiments, we have shown that our proposed method significantly accelerates the nearest neighbor search process.

Fast Online Hashing with Multi-Label Projection

Hashing has been widely researched to solve the large-scale approximate nearest neighbor search problem owing to its time and storage superiority. In recent years, a number of online hashing methods have emerged, which can update the hash functions to adapt to the new stream data and realize dynamic retrieval. However, existing online hashing methods are required to update the whole database with the latest hash functions when a query arrives, which leads to low retrieval efficiency with the continuous increase of the stream data. On the other hand, these methods ignore the supervision relationship among the examples, especially in the multi-label case. In this paper, we propose a novel Fast Online Hashing (FOH) method which only updates the binary codes of a small part of the database. To be specific, we first build a query pool in which the nearest neighbors of each central point are recorded. When a new query arrives, only the binary codes of the corresponding potential neighbors are updated. In addition, we create a similarity matrix which takes the multi-label supervision information into account and bring in the multi-label projection loss to further preserve the similarity among the multi-label data. The experimental results on two common benchmarks show that the proposed FOH can achieve dramatic superiority on query time up to 6.28 seconds less than state-of-the-art baselines with competitive retrieval accuracy.

High-Dimensional Approximate Nearest Neighbor Search: with Reliable and Efficient Distance Comparison Operations

Approximate K nearest neighbor (AKNN) search in the high-dimensional Euclidean vector space is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations (DCOs). For each operation, it scans full dimensions of an object and thus, runs in linear time wrt the dimensionality. To speed it up, we propose a randomized algorithm named ADSampling which runs in logarithmic time wrt the dimensionality for the majority of DCOs and succeeds with high probability. In addition, based on ADSampling we develop one generic and two algorithm-specific techniques as plugins to enhance existing AKNN algorithms. Both theoretical and empirical studies confirm that: (1) our techniques introduce nearly no accuracy loss and (2) they consistently improve the efficiency.