A sufficient condition for convergence of Mean Shift algorithm in any dimension, with radially symmetric, strictly positive definite kernels

Susovan Pal (EPITA)
December 10, 2021 — 11:00 — Location: Online


The mean shift (MS) is a non-parametric, density based, iterative algorithm that has been used to find the modes of an estimated probability density function (pdf). Although the MS algorithm has been widely used in many applications, such as clustering, image segmentation, and object tracking, a rigorous proof for its convergence in a fully general case is still missing. Two significant steps toward this direction were taken in a paper by Ghassabeh, that proved the convergence for Gaussian kernels in any dimensions, and also by the same author, who proved the convergence for one dimension for kernels with differentiable, strictly decreasing, convex profiles. As of now, we are not aware of any proof of convergence of the MS algorithm for fully general kernels. This paper/talk aims to give a sufficient condition for the convergence result for any dimensions, and for any strictly positive definite, smooth kernels. Some open questions for further research will also be addressed, with no rigorous mathematical detail known to the author.