Project Summary:

We propose to address the analysis and visualization of large networks via topological data analysis (TDA). Using TDA, we want to investigate new feature-extraction techniques for networks and use those features to build intuitive, informative, and interactive visualizations of the underlying data. In this proposal we identify the lack of explicit structure-preservation as a potential issue in existing graph visualization techniques and systems. We propose using TDA, which provides a strong theoretical basis for simplifying and summarizing complex data while still preserving critical underlying structures, to support interactive visualizations. Topological methods will provide a basis for task-oriented designs that allow us to control the volume of data to be displayed in visualizations, so users can develop faithful mental models of the data, facilitating information discovery. While the approaches we develop will be general, we will directly apply them to assist our domain collaborator in the area of connectomics.