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

Ery Arias-Castro, David Mason, Bruno Pelletier.

Year: 2016, Volume: 17, Issue: 43, Pages: 1−28


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.