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Single Linkage Clustering and Continuum Percolation

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  • Penrose, M. D.

Abstract

Suppose f is a probability density function in d dimensions, d >= 2. A single linkage a-cluster on a sample of size n from the density f is a connected component of the union of balls of volume a, centred at the sample points. Let [lambda]c be the percolation threshold above which a d-dimensional Poisson process of rate [lambda] has an unbounded 1-cluster. We show that for large n, the "big" single linkage ([lambda]c/(hn))-clusters can be used to detect population clusters, i.e., maximal connected sets of the form {x : f(x) >= h}. Here, a big cluster is one that contains a positive fraction of the sample points.

Suggested Citation

  • Penrose, M. D., 1995. "Single Linkage Clustering and Continuum Percolation," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 94-109, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:94-109
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    Cited by:

    1. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2001. "Cluster analysis: a further approach based on density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 441-459, June.

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