Summary
As part of the effort to (a) robustify the single link clustering method and (b) develop new inference approaches in clustering in the spirit of Bock (1985), we introduce upper and lower bounds for the length M n of the longest edge of the minimal spanning tree on n iid random variables drawn from a probability measure P, having Lebesgue density f. We prove that with probability converging to 1 as n → ∞:
where \( \delta = \inf \{ f(x),x\,\, \in \,\,\text{supp(P)\} ,}\,\Delta \,\, = \,\sup \{ f(x),x\,\, \in \,\text{supp(P)}\} \) and k L , k U are constants depending only on δsupp(P).
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References
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© 1996 Springer-Verlag Berlin · Heidelberg
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Tabakis, E. (1996). On the Longest Edge of the Minimal Spanning Tree. In: Gaul, W., Pfeifer, D. (eds) From Data to Knowledge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79999-0_22
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DOI: https://doi.org/10.1007/978-3-642-79999-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60354-2
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