PhD Defense by James Fairbanks
Dissertation Defense Announcement
Title: Graph Analysis Combining Numerical, Statistical, and Streaming Techniques
PhD Computational Science and Engineering
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Time: 9:00 am
Location: Klaus Advanced Computing Building 1212
Prof. David Bader (Advisor, School of Computational Science and Engineering, Georgia Tech)
Prof. Haesun Park (School of Computational Science and Engineering, Georgia Tech)
Prof. Richard Vuduc (School of Computational Science and Engineering, Georgia Tech)
Prof. Polo Chau (School of Computational Science and Engineering, Georgia Tech)
Prof. Dana Randall (School of Computer Science, Georgia Tech)
Graph analysis uses graph data collected on a physical, biological, or social
phenomena to shed light on the underlying dynamics and behavior of the agents
in that system. Many fields contribute to this topic including graph theory,
algorithms, statistics, machine learning, and linear algebra.
This dissertation advances a novel framework for dynamic graph analysis
that combines numerical, statistical, and streaming algorithms to provide deep
understanding into evolving networks. For example, one can be interested in the
changing influence structure over time. These disparate techniques each
contribute a fragment to understanding the graph; however, their combination
allows us to understand dynamic behavior and graph structure.
Spectral partitioning methods rely on eigenvectors for solving data analysis
problems such as clustering. Eigenvectors of large sparse systems must be
approximated with iterative methods. This dissertation analyzes how data
analysis accuracy depends on the numerical accuracy of the eigensolver. This
leads to new bounds on the residual tolerance necessary to guarantee correct
partitioning. We present a novel stopping criterion for spectral partitioning
guaranteed to satisfy the Cheeger inequality along with an empirical study of
the performance on real world networks such as web, social, and e-commerce networks.
This work bridges the gap between numerical analysis and computational data analysis.