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Title: Graph Analysis Combining Numerical, Statistical, and Streaming Techniques

James Fairbanks

PhD Computational Science and Engineering

School of Computational Science and Engineering

College of Computing

Georgia Institute of Technology

Date: 2016-03-28

Time: 9:00 am

Location: Klaus Advanced Computing Building 1212

Committee:

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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)

Abstract:

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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.