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A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree

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  • González-Barrios, José María
  • Quiroz, Adolfo J.

Abstract

We present a procedure for the identification of clusters in multivariate data sets, based on the comparison between the k nearest neighbors graph, Gk, and the minimal spanning tree, MST. Our key statistic is the random quantity the smallest k such that Gk contains the MST. Under regularity assumptions, we show that for i.i.d. data from a density on with compact support having one connected component, , where n denotes sample size, a bound that seems to be sharp, according to simulations. This leads to a consistent test for the identification of crisp clusters. We illustrate the use of our procedure with an example.

Suggested Citation

  • González-Barrios, José María & Quiroz, Adolfo J., 2003. "A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 23-34, March.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:1:p:23-34
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    References listed on IDEAS

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    1. Brito, María R. & Quiroz, Adolfo J. & Yukich, J. E., 2002. "Graph-Theoretic Procedures for Dimension Identification," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 67-84, April.
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