Fukunaga and Hostetler proposed, in the 1970s, to cluster points in space according to the gradient flow of the underlying sampling density. Although their work has generated a good amount of interest, including in recent years, the theoretical underpinnings of this proposal have not been fully developed. Our contribution to the effort is multi-pronged. First, we describe how this definition of clustering coincides with the equally well-known definition of Hartigan based on the density level sets — also proposed in the 1970s. These two approaches to clustering may thus be considered together under the umbrella name of “modal clustering” — which has been in use for a while. We then present novel consistency results for the main modal clustering methods.
Apr 25, 2022, 12:30 pm – 1:30 pm