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CME 510: Linear Algebra Optimization Seminar

Speaker: Christine Klymko, Lawrence Livermore National Laboratory

Title:Detection of highly-cyclic communities in directed networks

Abstract: Many large, real-world complex network have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological structure, even when they overlap with other communities, is a powerful capability that would provide novel avenues of focusing in on structure of interest. In this work we consider extracting highly-cyclic regions of directed graphs (digraphs). We demonstrate that embeddings derived from complex-valued eigenvectors associated with stochastic propagator eigenvalues near roots of unity are well-suited for this purpose. We prove several fundamental theoretic results demonstrating the connection between these eigenpairs and the presence of highly-cyclic structure and we demonstrate the use of these vectors on a few real-world examples.
 
Bio: Christine Klymko is currently a postdoctoral researcher at the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. She received her PhD in Computational Mathematics from the Department of Mathematics and Computer Science at Emory University in 2014. During her doctoral studies, she spent summers at Oak Ridge National Laboratory and Sandia National Laboratories. Her research interests include numerical linear algebra, graph algorithms, data mining, matrix analysis, machine learning, and scientific computing.
Location: 

Y2E2-101

Organizer: 
Michael Saunders
Date: 
Thursday, April 7, 2016 -
4:30pm to 5:45pm