On Efficient Retrieval of Top Similarity Vectors

Tan, Shulong; Xu, Zhaozhuo; Li, Ping

doi:10.18653/v1/d19-1527

Cited by 17 publications

(21 citation statements)

References 34 publications

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“…A Voronoi diagram for a point set is defined in terms of a similarity measure, which is the inner product function ⟨•, •⟩ here. Prior work has investigated the relationships between the inner-product Voronoi diagram and graph-based maximum inner product search [34,40,47]. We will first consider using the inner-product Voronoi diagram for coreset construction in this work.…”

Section: Inner-product Voronoi Diagrammentioning

confidence: 99%

“…Formally, it is an undirected graph G( ) = ( , ) where = , and there exists an edge { , } ∈ if and only if ( ) ∩ ( ) ≠ ∅. The number of edges in G( ) grows exponentially with and building an exact IPDG is often not computationally feasible when > 3 [40]. Nevertheless, the IPDG G( ) of point set can be built from the convex hull CH ( ) efficiently in R 2 or R 3 since the edges in CH ( ) exactly correspond to the edges in G( ).…”

Section: Inner-product Voronoi Diagrammentioning

confidence: 99%

“…□ Remark: Since constructing the exact IPDG of a point set is computationally intensive when > 3, we consider using an approximate IPDG instead for dominance graph construction. A practical approach to building an approximate IPDG proposed in [40] is used in our implementation. We show that using an approximate IPDG G( ) instead of the exact IPDG G( ) does not affect the correctness of DSMC-i.e., the solution of DSMC computed from a dominance graph built based on G( ) is still a valid -coreset.…”

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confidence: 99%

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Minimum Coresets for Maxima Representation of Multidimensional Data

Wang

Mathioudakis

et al. 2021

Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Coresets are succinct summaries of large datasets such that, for a given problem, the solution obtained from a coreset is provably competitive with the solution obtained from the full dataset. As such, coreset-based data summarization techniques have been successfully applied to various problems, e.g., geometric optimization, clustering, and approximate query processing, for scaling them up to massive data. In this paper, we study coresets for the maxima representation of multidimensional data: Given a set of points in R , where is a small constant, and an error parameter ∈ (0, 1), a subset ⊆ is an -coreset for the maxima representation of iff the maximum of is an -approximation of the maximum of for any vector ∈ R , where the maximum is taken over the inner products between the set of points ( or ) and . We define a novel minimum -coreset problem that asks for an -coreset of the smallest size for the maxima representation of a point set. For the two-dimensional case, we develop an optimal polynomial-time algorithm for the minimum -coreset problem by transforming it into the shortest-cycle problem in a directed graph. Then, we prove that this problem is NP-hard in three or higher dimensions and present polynomial-time approximation algorithms in an arbitrary fixed dimension. Finally, we provide extensive experimental results on both real and synthetic datasets to demonstrate the superior performance of our proposed algorithms. CCS CONCEPTS• Theory of computation → Data structures and algorithms for data management; Computational geometry.

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Section: Inner-product Voronoi Diagrammentioning

confidence: 99%

Section: Inner-product Voronoi Diagrammentioning

confidence: 99%

mentioning

confidence: 99%

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Minimum Coresets for Maxima Representation of Multidimensional Data

Wang

Mathioudakis

et al. 2021

Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…Then the methods for NNS problem such as Locality-Sensitive hash [49] and partition trees [29] can be applied to solve the converted problem. The signiicant superiorities of graph based methods for NNS problem also encourage researchers to solve MIPS problem by routing on the proximity graph [46,58,66]. The database is mapped to a graph such that each data point in the database is represented by a vertex on the graph and the relevance among data points is exhibited by the edges.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement Routing on Proximity Graph for Efficient Recommendation

Cao

Lian

Xiting

et al. 2023

ACM Trans. Inf. Syst.

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We focus on Maximum Inner Product Search (MIPS), which is an essential problem in many machine learning communities. Given a query, MIPS finds the most similar items with the maximum inner products. Methods for Nearest Neighbor Search (NNS) which is usually defined on metric space don’t exhibit the satisfactory performance for MIPS problem since inner product is a non-metric function. However, inner products exhibit many good properties compared with metric functions, such as avoiding vanishing and exploding gradients. As a result, inner product is widely used in many recommendation systems, which makes efficient Maximum Inner Product Search a key for speeding up many recommendation systems. Graph based methods for NNS problem show the superiorities compared with other class methods. Each data point of the database is mapped to a node of the proximity graph. Nearest neighbor search in the database can be converted to route on the proximity graph to find the nearest neighbor for the query. This technique can be used to solve MIPS problem. Instead of searching the nearest neighbor for the query, we search the item with maximum inner product with query on the proximity graph. In this paper, we propose a reinforcement model to train an agent to search on the proximity graph automatically for MIPS problem if we lack the ground truths of training queries. If we know the ground truths of some training queries, our model can also utilize these ground truths by imitation learning to improve the agent’s search ability. By experiments, we can see that our proposed mode which combines reinforcement learning with imitation learning shows the superiorities over the state-of-the-art methods.

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“…One area of active research is to improve the quality of "recalls" (of ads) before calling the CTR model. For example, Baidu has recently shared such a technical paper [20] to the community, which was built on top of fast near neighbor search algorithms [55,64] and maximum inner product search techniques [51,56].…”

Section: Introductionmentioning

confidence: 99%

AIBox

Zhao¹,

Zhang²,

Xie

et al. 2019

Proceedings of the 28th ACM International Conference on Information and Knowledge Management

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As one of the major search engines in the world, Baidu's Sponsored Search has long adopted the use of deep neural network (DNN) models for Ads click-through rate (CTR) predictions, as early as in 2013. The input futures used by Baidu's online advertising system (a.k.a. "Phoenix Nest") are extremely high-dimensional (e.g., hundreds or even thousands of billions of features) and also extremely sparse. The size of the CTR models used by Baidu's production system can well exceed 10TB. This imposes tremendous challenges for training, updating, and using such models in production. For Baidu's Ads system, it is obviously important to keep the model training process highly efficient so that engineers (and researchers) are able to quickly refine and test their new models or new features. Moreover, as billions of user ads click history entries are arriving every day, the models have to be retrained rapidly because CTR prediction is an extremely time-sensitive task. Baidu's current CTR models are trained on MPI (Message Passing Interface) clusters, which require high fault tolerance and synchronization that incur expensive communication and computation costs. And, of course, the maintenance costs for clusters are also substantial. This paper presents AIBox, a centralized system to train CTR models with tens-of-terabytes-scale parameters by employing solidstate drives (SSDs) and GPUs. Due to the memory limitation on GPUs, we carefully partition the CTR model into two parts: one is suitable for CPUs and another for GPUs. We further introduce a bi-level cache management system over SSDs to store the 10TB parameters while providing low-latency accesses. Extensive experiments on production data reveal the effectiveness of the new system. AIBox has comparable training performance with a large MPI cluster, while requiring only a small fraction of the cost for the cluster. CCS CONCEPTS • Information systems → Online advertising; • Hardware → Analysis and design of emerging devices and systems.

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On Efficient Retrieval of Top Similarity Vectors

Cited by 17 publications

References 34 publications

Minimum Coresets for Maxima Representation of Multidimensional Data

Minimum Coresets for Maxima Representation of Multidimensional Data

Reinforcement Routing on Proximity Graph for Efficient Recommendation

AIBox

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