A fresh look at mean-shift based modal clustering

Modal clustering is an unsupervised learning technique where cluster centers are identified as the local maxima of nonparametric probability density estimates. A natural algorithmic engine for the computation of these maxima is the mean shift procedure, which is essentially an iteratively computed chain of local means. We revisit this technique, focusing on its link to kernel density gradient estimation, in this course proposing a novel concept for bandwidth selection based on the concept of a critical bandwidth. Furthermore, in the one-dimensional case, an inverse version of the mean shift is developed to provide a novel approach for the estimation of antimodes, which is then used to identify cluster boundaries. A simulation study is provided which assesses, in the univariate case, the classification accuracy of the mean-shift based clustering approach. Three (univariate and multivariate) examples from the fields of philately, engineering, and imaging, illustrate how modal clusterings identified through mean shift based methods relate directly and naturally to physical properties of the data-generating system. Solutions are proposed to deal computationally efficiently with large data sets.