On the convergence and applications of mean shift type algorithms

Mean shift (MS) and subspace constrained mean shift (SCMS) algorithms are iterative methods to find an underlying manifold associated with an intrinsically low dimensional data set embedded in a high dimensional space. Although the MS and SCMS algorithms have been used in many applications related to information and signal processing, a rigorous study of their convergence properties is still missing. This paper aims to fill some of the gaps between theory and practice. We present theoretical results about convergence of the MS and SCMS algorithms. As well, we discuss potential applications of the SCMS algorithm as a preprocessing step for noisy source vector quantization and nonlinear dimensionality reduction with noisy observations.