A0747
Title: Local depth functions and clustering
Authors: Giacomo Francisci - University of Ulm (Germany) [presenting]
Claudio Agostinelli - University of Trento (Italy)
Alicia Nieto-Reyes - Universidad de Cantabria (Spain)
Anand Vidyashankar - George Mason University (United States)
Abstract: Local depth functions are a generalization of depth functions and are used to capture local features of multivariate distributions. When the distribution is absolutely continuous, rescaled local depth functions converge uniformly to the underlying density. Under appropriate regularity conditions, their derivatives also converge. Using these results and a gradient system analysis, it is developed a clustering algorithm based on identification of (i) the modes and (ii) the basis of attractions of the modes via the gradient system. The algorithm is consistent in the sense that the probability distance between true and empirical clusters converges to zero as the sample size diverges to infinity. To show this, it is established a Bernstein-type inequality for deviations between the centered and rescaled local depth functions. Finally, the finite sample performance of the algorithm is investigated via Monte Carlo simulations.
