Graph analysis combining numerical, statistical, and streaming techniques

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.Ph.D

XXV Congreso Argentino de Ciencias de la Computación - CACIC 2019: libro de actas

Trabajos presentados en el XXV Congreso Argentino de Ciencias de la Computación (CACIC), celebrado en la ciudad de Río Cuarto los días 14 al 18 de octubre de 2019 organizado por la Red de Universidades con Carreras en Informática (RedUNCI) y Facultad de Ciencias Exactas, Físico-Químicas y Naturales - Universidad Nacional de Río CuartoRed de Universidades con Carreras en Informátic

XXV Congreso Argentino de Ciencias de la Computación - CACIC 2019: libro de actas

Trabajos presentados en el XXV Congreso Argentino de Ciencias de la Computación (CACIC), celebrado en la ciudad de Río Cuarto los días 14 al 18 de octubre de 2019 organizado por la Red de Universidades con Carreras en Informática (RedUNCI) y Facultad de Ciencias Exactas, Físico-Químicas y Naturales - Universidad Nacional de Río CuartoRed de Universidades con Carreras en Informátic