Title: Topological Analysis Of Wildfire Ignition Data

Program: Mathematics MS

Committee Chair: Michael Perlmutter

Commitee: Michael Perlmutter, Zach Teitler, Jens Harlander

Abstract: Topological Data Analysis (TDA) applies techniques from algebraic topology to extract qualitative geometric and topological features from complex datasets. This thesis presents foundational concepts in TDA, including simplicial complexes, nerves, filtrations, and persistent homology. It then demonstrates their application to problems in public resource allocation and wildfire classification. Coverage maps showing public accessibility to cooling centers in Austin, Texas and Boise, Idaho are created by performing persistent homology on witness complexes built from the geospatial data of each city. These maps can be used as a supplement for the Heat Vulnerability Index, or as a low-cost alternative in regions where demographic data is less readily available. The Mapper algorithm is applied to the high-dimensional Fire Program Analysis Fire-Occurrence Database-Attributes dataset to produce graph representations that preserve topological structure while providing interpretable visualizations of the data. Several machine learning models are then used for the classification of wildfire ignition causes. Tree-based methods, particularly XGBoost, achieve higher predictive accuracy and lower computational cost than the neural network architectures considered. These results illustrate the utility of topological methods for both exploratory data analysis and practical decision making, and suggest that the integration of topological features, using methods such as persistence landscapes, provides a promising direction for the enhancement of machine learning models in future work.