The Annals of Statistics

Asymptotic Distributions for Clustering Criteria

J. A. Hartigan

Full-text: Open access

Abstract

A set of observations is partitioned into $k$ clusters by optimizing a clustering criterion $W$. The asymptotic distribution of this clustering criterion may be determined simply in certain cases where the optimal sample partition differs negligibly from the optimal population partition. Detailed proofs are given in the one-dimensional case when the clustering criterion to be minimized is within cluster sum of squares. The asymptotic distributions are used to compute approximate significance levels of tests for the presence of clusters, and of tests for bimodality.

Article information

Source
Ann. Statist., Volume 6, Number 1 (1978), 117-131.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344071

Digital Object Identifier
doi:10.1214/aos/1176344071

Mathematical Reviews number (MathSciNet)
MR461780

Zentralblatt MATH identifier
0377.62033

JSTOR
links.jstor.org

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Keywords
Clustering criteria tests for bimodality asymptotic distributions

Citation

Hartigan, J. A. Asymptotic Distributions for Clustering Criteria. Ann. Statist. 6 (1978), no. 1, 117--131. doi:10.1214/aos/1176344071. https://projecteuclid.org/euclid.aos/1176344071


Export citation