Hartigan Lecture.

John Hartigan identified as natural clusters in a Euclidean population, neighborhoods of modes of the population density. There has recently been much interest in spectral clustering using so called kernel matrices based on kernels, such as, the ones used in kernel density estimation We show, heuristically, a close relation between density contour clustering and spectral clustering using kernels as used in density estimation. We also prove a rather weak theorem supporting the heuristics and provide simulations supporting the theorem.