PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jason Morton, Manfred Denker.

Title:Stability of Density-Based Clustering
Seminar:Seminar on Probability and its Application
Speaker:Alessandro Rinaldo, Carnegie Mellon University
Abstract:
High density clusters can be characterized by the connected components of a level set $L(\lambda) = \{x:\ p(x)>\lambda\}$ of the underlying probability density function $p$ generating the data, at some appropriate level $\lambda\geq 0$. The complete hierarchical clustering can be characterized by a cluster tree ${\cal T}= \bigcup_{\lambda} L(\lambda)$. In this paper, we study the behavior of a density level set estimate $\widehat L(\lambda)$ and cluster tree estimate $\widehat{\cal{T}}$ based on a kernel density estimator with kernel bandwidth $h$. We define two notions of instability to measure the variability of $\widehat L(\lambda)$ and $\widehat{\cal{T}}$ as a function of $h$, and investigate the theoretical properties of these instability measures. This is joint work with Aarti Singh, Rebecca Nugent and Larry Wasserman.

Room Reservation Information

Room Number:MB106
Date:12 / 03 / 2010
Time:02:30pm - 03:25pm