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Practical Construction of k-Nearest Neighbor Graphs in Metric Spaces

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Experimental Algorithms (WEA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4007))

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Abstract

Let \(\mathbb{U}\) be a set of elements and d a distance function defined among them. Let NN k (u) be the k elements in \(\mathbb{U}-\{u\}\) having the smallest distance to u. The k-nearest neighbor graph (k nng) is a weighted directed graph \(G(\mathbb{U},E)\) such that E = {(u,v), v ∈ NN k (u)}. Several k nng construction algorithms are known, but they are not suitable to general metric spaces. We present a general methodology to construct k nngs that exploits several features of metric spaces. Experiments suggest that it yields costs of the form c 1 n 1.27 distance computations for low and medium dimensional spaces, and c 2 n 1.90 for high dimensional ones.

Supported in part by Millennium Nucleus Center for Web Research, Grant P04-067-F, Mideplan, Chile; and CONACyT, Mexico.

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Author information

Authors and Affiliations

  1. Center for Web Research, Dept. of Computer Science, University of Chile,  

    Rodrigo Paredes, Karina Figueroa & Gonzalo Navarro

  2. Escuela de Ciencias Físico-Matemáticas, Univ. Michoacana, Mexico

    Edgar Chávez & Karina Figueroa

Authors
  1. Rodrigo Paredes
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  2. Edgar Chávez
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  3. Karina Figueroa
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  4. Gonzalo Navarro
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Editor information

Editors and Affiliations

  1. Software Department, Edifici Omega, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Carme Àlvarez

  2. ALBCOM Research Group, Universitat Politècnica de Catalunya, Edifici Ω, Campus Nord, Jordi Girona, 1-3, 08034, Barcelona, Spain

    María Serna

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© 2006 Springer-Verlag Berlin Heidelberg

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Paredes, R., Chávez, E., Figueroa, K., Navarro, G. (2006). Practical Construction of k-Nearest Neighbor Graphs in Metric Spaces. In: Àlvarez, C., Serna, M. (eds) Experimental Algorithms. WEA 2006. Lecture Notes in Computer Science, vol 4007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11764298_8

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  • DOI: https://doi.org/10.1007/11764298_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34597-8

  • Online ISBN: 978-3-540-34598-5

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