(Georgia Institute of Technology, 2016-05-10)
Godbole, Pushkar J.
Agglomerative Clustering techniques work by recursively merging graph vertices into communities, to maximize a clustering quality metric. The metric of Modularity coined by Newman and Girvan, measures the cluster quality based on the premise that, a cluster has collections of vertices more strongly connected internally than would occur from random chance. Various fast and efficient algorithms for community detection based on modularity maximization have been developed for static graphs. However, since many (contemporary) networks are not static but rather evolve over time, the static approaches are rendered inappropriate for clustering of dynamic graphs. Modularity optimization in changing graphs is a relatively new field that entails the need to develop efficient algorithms for detection and maintenance of a community structure while minimizing the “Size of change” and computational effort. The objective of this work was to develop an efficient dynamic agglomerative clustering algorithm that attempts to maximize modularity while minimizing the “size of change” in the transitioning community structure. First we briefly discuss the previous memoryless dynamic reagglomeration approach with localized vertex freeing and illustrate its performance and limitations. Then
we describe the new backtracking algorithm followed by its performance results and observations. In experimental analysis of both typical and pathological cases, we evaluate and justify various backtracking and agglomeration strategies in context of
the graph structure and incoming stream topologies. Evaluation of the algorithm on social network datasets, including Facebook (SNAP) and PGP Giant Component networks shows significantly improved performance over its conventional static counterpart in terms of execution time, Modularity and Size of Change.
(Georgia Institute of Technology, 2016-03-31)
Fairbanks, James Paul
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.