Distance-based indexing for high-dimensional metric spaces

Bozkaya, Tolga; Ozsoyoglu, Meral

doi:10.1145/253260.253345

Cited by 229 publications

(162 citation statements)

References 12 publications

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“…11. Examples of methods that rely on this are the M-tree [77][78][79] (and its descendants), the MVP-tree [81] and D-index [50][51][52][53]101]. 12.…”

Section: B An Overview Of the Indexing Methodsmentioning

confidence: 99%

The Basic Principles of Metric Indexing

Hetland

2009

Studies in Computational Intelligence

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Summary. This chapter describes several methods of similarity search, based on metric indexing, in terms of their common, underlying principles. Several approaches to creating lower bounds using the metric axioms are discussed, such as pivoting and compact partitioning with metric ball regions and generalized hyperplanes. Finally, pointers are given for further exploration of the subject, including non-metric, approximate, and parallel methods.

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“…11. Examples of methods that rely on this are the M-tree [77][78][79] (and its descendants), the MVP-tree [81] and D-index [50][51][52][53]101]. 12.…”

Section: B An Overview Of the Indexing Methodsmentioning

confidence: 99%

The Basic Principles of Metric Indexing

Hetland

2009

Studies in Computational Intelligence

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“…In the discrete case we have: Burkhard-Keller Tree (BKT) [10], Fixed Queries Tree (FQT) [4], Fixed-Height FQT (FHQT) [4,3], and Fixed Queries Array (FQA) [14]. In the continuous case we have: Vantage-Point Tree (VPT) [42,17,39], Multi-Vantage-Point Tree (MVPT) [9,8], Excluded Middle Vantage Point Forest (VPF) [43], Approximating Eliminating Search Algorithm (AESA) [40], and Linear AESA (LAESA) [29]. For a comprehensive description of these algorithms see [16].…”

Section: Pivot-based Algorithmsmentioning

confidence: 99%

t-Spanners for metric space searching

Navarro¹,

Paredes²,

Chávez³

2007

Data & Knowledge Engineering

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The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a t-spanner G ′ (V, E) as the representation of the metric database. A t-spanner is a subgraph G ′ (V, E) of a graph G(V, A), such that E ⊆ A and G ′ approximates the shortest path costs over G within a precision factor t.Our key idea is to regard the t-spanner as an approximation to the complete graph of distances among the objects, and to use it as a compact device to simulate the large matrix of distances required by successful search algorithms such as AESA. The t-spanner properties imply that we can use shortest paths over G ′ to estimate any distance with bounded error factor t.For this sake, several t-spanner construction, updating, and search algorithms are proposed and experimentally evaluated. We show that our technique is competitive against current approaches. For example, in a metric space of documents our search time is only 9% over AESA, yet we need just 4% of its space requirement. Similar results are obtained in other metric spaces.Finally, we conjecture that the essential metric space property to obtain good tspanner performance is the existence of clusters of elements, and enough empirical evidence is given to support this claim. This property holds in most real-world metric spaces, so we expect that t-spanners will display good behavior in most practical applications. Furthermore, we show that t-spanners have a great potential for improvements.

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“…For instance, in M-tree above bounds are computed as max{d(vi, vr) − r(vr), 0} and d(vi, vr) + r(vr), respectively [CPZ97]. Simple calculations are similarly required for other metric trees [Chi94,Bri95,BO97], as well as for spatial access methods, such as R-tree (see [RKV95]). …”

Section: Db(vi Reg(n )) = Dmin(vi Reg(n )) If S F Is Monotonic Incrmentioning

confidence: 99%

Processing complex similarity queries with distance-based access methods

Ciaccia

Patella

Zezula

1998

Lecture Notes in Computer Science

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Abstract. Efficient evaluation of similarity queries is one of the basic requirements for advanced multimedia applications. In this paper, we consider the relevant case where complex similarity queries are defined through a generic language L and whose predicates refer to a single feature F . Contrary to the language level which deals only with similarity scores, the proposed evaluation process is based on distances between feature values -known spatial or metric indexes use distances to evaluate predicates. The proposed solution suggests that the index should process complex queries as a whole, thus evaluating multiple similarity predicates at a time. The flexibility of our approach is demonstrated by considering three different similarity languages, and showing how the M-tree access method has been extended to this purpose. Experimental results clearly show that performance of the extended M-tree is consistently better than that of state-of-the-art search algorithms.

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Distance-based indexing for high-dimensional metric spaces

Cited by 229 publications

References 12 publications

The Basic Principles of Metric Indexing

The Basic Principles of Metric Indexing

t-Spanners for metric space searching

Processing complex similarity queries with distance-based access methods

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