The Population Goal of Modal Clustering

• Activity Number: 318
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jose E. Chacon*+
• Companies: Universidad De Extremadura
• Keywords: cluster analysis ; Morse theory ; modal clustering ; nonparametric ; population goal

Abstract

The task of clustering data to form homogeneous groups has been extensively studied. It has equally attracted researchers from Statistics and Computer Science, thus originating solutions from a wide variety of viewpoints. In this talk we focus on a nonparametric approach, that relies on the statistical notion of modal clustering, in which different clusters correspond to the modes (i.e., local maxima) of the probability density generating the data. Within this methodology, it is not straighforward how to explicitly specify the population goal, or "ground truth", in a precise way. Here we present a clear formulation of the population goal of modal clustering making use of some tools from Differential Geometry.