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Heuristics for Computing k-Nearest Neighbors Graphs

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Computer Science – CACIC 2019 (CACIC 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1184))

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Abstract

The k-Nearest Neighbors Graph (kNNG) consists of links from an object to its k-Nearest Neighbors. This graph is of interest in diverse applications ranging from statistics, machine learning, clustering and outlier detection, computational biology, and even indexing. Obtaining the kNNG is challenging because intrinsically high dimensional spaces are known to be unindexable, even in the approximate case. The cost of building an index is not well amortized over just all the objects in the database. In this paper, we introduce a method to compute the kNNG without building an index. While our approach is sequential, we show experimental evidence that the number of distance computations is a fraction of the \(n^2/2\) used in the naïve solution. We make heavy use of the notion of pivot, that is, database objects with full distance knowledge to all other database objects. From a group of pivots, it is possible to infer upper bounds of distance to other objects.

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Notes

  1. 1.

    At http://www.dimacs.rutgers.edu/Challenges/Sixth/software.html.

  2. 2.

    At http://www.dbs.informatik.uni-muenchen.de/~seidl/DATA/histo112.112682.gz.

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Author information

Authors and Affiliations

  1. Departamento de Informática, Universidad Nacional de San Luis, San Luis, Argentina

    Verónica Ludueña & Nora Reyes

  2. Centro de Investigación Científica y de Educación Superior de Ensenada, Ensenada, Mexico

    Edgar Chávez

Authors
  1. Edgar Chávez
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  2. Verónica Ludueña
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  3. Nora Reyes
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Corresponding author

Correspondence to Verónica Ludueña .

Editor information

Editors and Affiliations

  1. RedUNCI Chair, National University of La Plata, La Plata, Argentina

    Patricia Pesado

  2. National University of Río Cuarto, Río Cuarto, Argentina

    Marcelo Arroyo

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Chávez, E., Ludueña, V., Reyes, N. (2020). Heuristics for Computing k-Nearest Neighbors Graphs. In: Pesado, P., Arroyo, M. (eds) Computer Science – CACIC 2019. CACIC 2019. Communications in Computer and Information Science, vol 1184. Springer, Cham. https://doi.org/10.1007/978-3-030-48325-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-48325-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-48324-1

  • Online ISBN: 978-3-030-48325-8

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