Single Linkage Clustering and Continuum Percolation

✍ Scribed by M.D. Penrose

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 617 KB
• Volume: 53
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1995.1026

✦ Synopsis

Suppose (f) is a probability density function in (d) dimensions. (d \geqslant 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_{i}) be the percolation threshold above which a (d)-dimensional Poisson process of rate (i) has an unbounded 1-cluster. We show that for large (n). the "big" single linkage (\left(\lambda_{c}(h n)\right)) clusters can be used to detect population clusters. i.e., maximal connected sets of the form ({x: f(x) \geqslant h}). Here, a big cluster is one that contains a positive fraction of the sample points. ' 1995 Academic Press. Inc.