Fast Nonparametric Density-Based Clustering of Large Data Sets Using a Stochastic Approximation Mean-Shift Algorithm.

Abstract

Mean-shift is an iterative procedure often used as a nonparametric clustering algorithm that defines clusters based on the modal regions of a density function. The algorithm is conceptually appealing and makes assumptions neither about the shape of the clusters nor about their number. However, with a complexity of O(n²) per iteration, it does not scale well to large data sets. We propose a novel algorithm which performs density-based clustering much quicker than mean-shift, yet delivering virtually identical results. This algorithm combines subsampling and a stochastic approximation procedure to achieve a potential complexity of O(n) at each step. Its convergence is established. Its performances are evaluated using simulations and applications to image segmentation, where the algorithm was tens or hundreds of times faster than mean-shift, yet causing negligible amounts of clustering errors. The algorithm can be combined with existing approaches to further accelerate clustering.