Koç University, Mathematics Seminar

Date & Time: Tuesday, October 25, 16:00-17:00

Place: SCI 103

Speaker:  Selim Bahadır, Koç University

Title: Subdigraph Counts in Random k Nearest Neighbor Digraphs

Abstract:

We study the number of copies of a given digraph in k nearest neighbor (kNN) digraph of the data from a random point process in $\mathbb{R}^d$. Based on the asymptotic theory for functionals of point sets under homogeneous Poisson process (HPP) and uniform binomial process, we provide a general result for the asymptotic behavior of subdigraph counts and as corollaries, we obtain asymptotic results for the number of vertices with fixed indegree, the number of shared kNN pairs and the number of reflexive kNN's in a kNN digraph. Moreover, we use the method to analyze  kNN contingency tables for several classes under HPP.

 

Speaker's Brief Biography: Selim Bahadır obtained his B.S. degree from Bilkent University in 2007, his M.S. degree from University of California Los Angeles in 2009 and his Ph.D. degree from Koç University in 2016. His research interests lie within the intersection of probability theory, mathematical statistics, graph theory and spatial data analysis.