A0563
Title: Dynamic topological data analysis on time varying trees and cycles
Authors: Moo K Chung - University of Wisconsin-Madison (United States) [presenting]
Hernando Ombao - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Sixtus Dakurah - University of Wisconsin-Madison (United States)
Abstract: Persistent homology has been successfully applied to various static graphs and becoming a standard analysis tool. However, it is still not obvious how the method can be used in dynamically changing graphs over time. The challenge is obtaining continuous topological features over time, which might be contradictory since topological features are discrete and expected to be discontinued. We propose a coherent dynamic topological data analysis based on the newly discovered birth-death decomposition of graphs. By ignoring higher-dimensional topological features, it is possible to develop a mathematically coherent dynamic-TDA framework for time-varying graphs. The method is applied to quantify how the maximum spanning trees of the functional brain network of humans are topologically changing over time. We address various statistical challenges in tree and cycle modeling.
