Establishing Topological Data Analysis: A Comparison of Visualization Techniques
Tanmay Kotha · Digital Commons - University of South Florida (University of South Florida) · 2020
When visualizing data, we would like to convey both the data and the uncertainty associated with it. There are many incentives to do this, ranging from hurricane path projection to geographical surveys. Important decision making tasks rely upon humans perceiving a clear picture of the data and having confidence in their decisions. Topological Data Analysis has the potential to visualize the data as features or hierarchies in ways that are familiar to human intuition, and thus could help us convey the variation associated with uncertainty. In this thesis, we evaluate four visualization techniques: color maps, isocontours, Reeb graphs, and persistence diagrams, that each demonstrate some level of topological representation of the data. We build and run a user study evaluating the perception of various Gaussian signals applied on 3D models using each of the visualization techniques, and measure how effectively they each portray positional and amplitude variations. We show that for positional variation, the topology-based Reeb graph visualization shows higher accuracy than the other types of visualizations. For amplitude variation, the least topologically-oriented technique, color maps, demonstrated the highest accuracy. In terms of confidence, we show high levels of confidence in decision making for all techniques, except for color maps. These results take an important step towards understanding what topology-based tools are best to use under various data configuration scenarios.