Estimating the number of clusters | Zendy

Cuevas Antonio | Zendy; Febrero Manuel | Zendy; Fraiman Ricardo | Zendy

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Estimating the number of clusters

Author(s) -

Cuevas Antonio,

Febrero Manuel,

Fraiman Ricardo

Publication year - 2000

Publication title -

canadian journal of statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.804

H-Index - 51

eISSN - 1708-945X

pISSN - 0319-5724

DOI - 10.2307/3315985

Subject(s) - estimator , nonparametric statistics , computation , mathematics , constant (computer programming) , random variate , cluster (spacecraft) , set (abstract data type) , function (biology) , population , data set , algorithm , probability density function , statistics , computer science , combinatorics , random variable , demography , sociology , evolutionary biology , biology , programming language

Hartigan (1975) defines the number q of clusters in a d ‐variate statistical population as the number of connected components of the set { f > c}, where f denotes the underlying density function on R d and c is a given constant. Some usual cluster algorithms treat q as an input which must be given in advance. The authors propose a method for estimating this parameter which is based on the computation of the number of connected components of an estimate of { f > c}. This set estimator is constructed as a union of balls with centres at an appropriate subsample which is selected via a nonparametric density estimator of f . The asymptotic behaviour of the proposed method is analyzed. A simulation study and an example with real data are also included.

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