DMS Colloquium: Dr. Wanli Qiao

Speaker: Dr. Wanli Qiao (George Mason University)

Title: Connection and Consistency of Modal Clustering Methods 

Abstract: In the 1970s, Fukunaga and Hostetler put forward the idea of clustering points in space based on the gradient flow of the underlying sampling density. Despite generating significant interest, the theoretical basis of their proposal has not been fully developed, even in recent years. Our contribution to this effort is twofold. Firstly, we demonstrate how this clustering definition aligns with Hartigan's well-known definition, which also emerged in the 1970s, based on density level sets. These two approaches to clustering can thus be jointly referred to as "modal clustering," a term that has been in use for some time. Secondly, we present new consistency results for the main modal clustering methods. 

Faculty host: Guanqun Cao

Short Bio

Wanli Qiao is an Associate Professor in the Department of Statistics at George Mason University, where he also serves as the graduate program director. His research focuses on statistical inference, probability theory and computational algorithms related to geometric data analysis, which are applied towards analyzing the geometric and topological structures of molecular energy landscapes. His research is supported by the National Science Foundation.