Estimating the number of clusters
Antonio Cuevas, Manuel Febrero–Bande, Ricardo Fraiman · Canadian Journal of Statistics · 2000
Abstract Hartigan (1975) defines the numberqof clusters in ad‐variate statistical population as the number of connected components of the set {f> c}, wherefdenotes the underlying density function on Rdandcis a given constant. Some usual cluster algorithms treatqas 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 off. The asymptotic behaviour of the proposed method is analyzed. A simulation study and an example with real data are also included.