Distance-Based Index Structures for Fast Similarity Search

Rachkovskij, Dmitri A.

doi:10.1007/s10559-017-9966-y

“…We note that the index structures for the Hamming distance [28,116] work with vectors of moderate dimension (up to hundreds), and for binary sparse high dimensional vectors Jaccard similarity index structures are used [147,2,27,29]. A survey of these and other similar index structures is presented in the forthcoming [133], see also [132] for another type of index structures. модифікації значень ваг міжнейронних зв'язків, які існують між всіма нейронами (повнозв'язні мережі).…”

Section: Discussionmentioning

confidence: 99%

“…Note that such data representation schemes by similarity preserving binary vectors have been developed for objects represented by various data types, mainly for (feature) vectors (see survey in [131]), but also for structured data types such as sequences [102,72,85,86] and graphs [127,128,148,136,62,134]. A significant part of this research is developed in the framework of distributed representations [45,76,106,126,89], including binary sparse distributed representations [102,98,103,127,128,113,114,137,138,139,148,135,136,61,134,129,130,131,132,31,33] and dense distributed representations [75,76] (see [82,84,87,88,83] for examples of their applications).…”

Section: Generalization In Namsmentioning

confidence: 99%

Neural Autoassociative Memories for Binary Vectors: A Survey

Gritsenko¹,

Rachkovskij²,

Frolov³

et al. 2017

Kibern. vyčisl. teh.

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Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension.The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons).Scope. The survey is focused mainly on the networks of Hopfield, Willshaw and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We discuss not only autoassociative memory, but also the generalization properties of these networks. We also consider neural networks with higher-order connections and networks with a bipartite graph structure for non-binary data with linear constraints.Conclusions. In conclusion we discuss the relations to similarity search, advantages and drawbacks of these techniques, and topics for further research. An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search, in particular for the case of very high dimensional vectors. Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension.The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons).Scope. The survey is focused mainly on the networks of Hopfield, Willshaw and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We (Online), ISSN 0454-9910 (Print). Киб. и выч. техн. 2017. № 2 (188) 6 discuss not only autoassociative memory, but also the generalization properties of these networks. We also consider neural networks with higher-order connections and networks with a bipartite graph structure for non-binary data with linear constraints.Conclusions. In conclusion we discuss the relations to similarity search, advantages and drawbacks of these techniques, and topics for further research. An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search, in particular for the case of very high dimensional vectors. ISSN 2519-2205 (Online), ISSN 0454-9910 (Print). Киб...

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“…We note that the index structures for the Hamming distance [28,116] work with vectors of moderate dimension (up to hundreds), and for binary sparse high dimensional vectors Jaccard similarity index structures are used [147,2,27,29]. A survey of these and other similar index structures is presented in the forthcoming [133], see also [132] for another type of index structures. При подаче на вход автоассоциативной памяти искаженных вариантов запомненных в ней векторов осуществляется извлечение (восстановление) ближайшего запомненного вектора.…”

Section: Discussionunclassified

“…Note that such data representation schemes by similarity preserving binary vectors have been developed for objects represented by various data types, mainly for (feature) vectors (see survey in [131]), but also for structured data types such as sequences [102,72,85,86] and graphs [127,128,148,136,62,134]. A significant part of this research is developed in the framework of distributed representations [45,76,106,126,89], including binary sparse distributed representations [102,98,103,127,128,113,114,137,138,139,148,135,136,61,134,129,130,131,132,31,33] and dense distributed representations [75,76] (see [82,84,87,88,83] for examples of their applications).…”

Section: Generalization In Namsmentioning

confidence: 99%

Untitled

2017

Kibern. vyčisl. teh.

0

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Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension. The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons). Scope. The survey is focused mainly on the networks of Hopfield, Willshaw and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We 5

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“…A metric space is a general space that makes no requirement of any particular data representation, but only a distance function that satisfies the four properties, namely non-negativity, identity, symmetry and triangle inequality (Definition 1, Section 3). A number of metric-space indexing methods have been proposed in the literature to accelerate similarity query processing [2], [3], [4], [5], [6]. However, these indexing methods that are based on tree-like structures are increasingly challenged by the rapidly growing volume and complexity of data.…”

Section: Introductionmentioning

confidence: 99%

A Learned Index for Exact Similarity Search in Metric Spaces

Tian¹,

Yan²,

Xin³

et al. 2022

Preprint

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Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index has been explored actively to replace or supplement traditional index structures with machine learning models to reduce storage and search costs. However, accurate and efficient similarity query processing in high-dimensional metric spaces remains to be an open challenge. In this paper, a novel indexing approach called LIMS is proposed to use data clustering and pivot-based data transformation techniques to build learned indexes for efficient similarity query processing in metric spaces. The underlying data is partitioned into clusters such that each cluster follows a relatively uniform data distribution. Data redistribution is achieved by utilizing a small number of pivots for each cluster. Similar data are mapped into compact regions and the mapped values are totally ordinal. Machine learning models are developed to approximate the position of each data record on the disk. Efficient algorithms are designed for processing range queries and nearest neighbor queries based on LIMS, and for index maintenance with dynamic updates. Extensive experiments on real-world and synthetic datasets demonstrate the superiority of LIMS compared with traditional indexes and state-of-the-art learned indexes.

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Distance-Based Index Structures for Fast Similarity Search

Cited by 16 publications

References 110 publications

Neural Autoassociative Memories for Binary Vectors: A Survey

Neural Autoassociative Memories for Binary Vectors: A Survey

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A Learned Index for Exact Similarity Search in Metric Spaces

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