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 λc be the percolation threshold above which a d-dimensional Poisson process of rate λ has an unbounded 1-cluster. We show that for large n, the "big" single linkage (λc/(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. © 1995 Academic Press Inc.
CITATION STYLE
Penrose, M. D. (1995). Single linkage clustering and continuum percolation. Journal of Multivariate Analysis, 53(1), 94–109. https://doi.org/10.1006/jmva.1995.1026
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