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 |