Density-Based Clustering Using a Stochastic Approximation Mean-Shift Algorithm

• Activity Number: 295
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ollivier Hyrien*+
• Companies: University of Rochester
• Keywords: Robbins-Monro Stochastic approximation ; Large data sets ; Image segmentation

Abstract

The mean-shift is a non-parametric clustering algorithm that defines clusters based on the modal regions of a kernel density estimate of the data. The algorithm is conceptually appealing and makes assumptions neither about the shape of the clusters nor about their number. Its applicability to large data sets, however, is limited by the fact that the complexity of each iteration is O(n^2). In order to accelerate clustering, we propose to modify the algorithm by using a Robbins-Monro procedure. Each step of the stochastic approximation mean-shift algorithm achieves a theoretical complexity of O(n). Convergence of the algorithm is established. Its performance is evaluated using simulations and applications to image segmentation.