On the Estimation of the Gradient Lines of a Density and the Consistency of the Mean-Shift Algorithm

Ery Arias-Castro (1) , Bruno Pelletier (2, 3) , David D.M. Mason (4)

1 MATH - UC San Diego - Department of Mathematics [Univ California San Diego]
2 LABORATOIRE DE STATISTIQUES - Laboratoire de statistiques, Université Rennes 2
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Applied Economics and Statistics

We consider the problem of estimating the gradient lines of a density, which can be used to cluster points sampled from that density, for example via the mean-shift algorithm of Fukunaga and Hostetler (1975). We prove general convergence bounds that we then specialize to kernel density estimation.

Mots clés: mean-shift; gradient lines; density estimation; nonparametric clustering

Domaines: Statistiques [math.ST]

Ery Arias-Castro, Bruno Pelletier, David D.M. Mason. On the Estimation of the Gradient Lines of a Density and the Consistency of the Mean-Shift Algorithm. Journal of Machine Learning Research, 2016, 17 (43), pp.1-28. ⟨hal-01314654⟩