Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm

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.