  The mean shift (MS) algorithm is a nonparametric method used to cluster
sample points and find the local modes of kernel density estimates, using an
idea based on iterative gradient ascent. In this paper we develop a
mean-shift-inspired algorithm to estimate the modes of regression functions and
partition the sample points in the input space. We prove convergence of the
sequences generated by the algorithm and derive the non-asymptotic rates of
convergence of the estimated local modes for the underlying regression model.
We also demonstrate the utility of the algorithm for data-enabled discovery
through an application on biomolecular structure data. An extension to subspace
constrained mean shift (SCMS) algorithm used to extract ridges of regression
functions is briefly discussed.
