Topological data analysis for driver behavior classification driven by vehicle trajectory data

With urbanization and rising vehicle numbers, road safety has become increasingly critical. Robust, trajectory-level risk assessment is essential for next-generation active safety systems, accident prevention, autonomous driving, and intelligent transportation networks. This paper presents a novel framework for driver behavior classification using Topological Data Analysis (TDA) — a mathematical approach for analyzing high-dimensional data — via persistent homology applied to vehicle trajectory data. Traditional methods often struggle with the complexity of such data, but TDA captures topological features that reveal subtle, meaningful behavioral patterns. Using the HighD dataset, we train a class-weighted XGBoost classifier on persistence image (PI) features, achieving 96.8% overall accuracy, macro-F${}_1$ = 0.93, and retaining 87% F${}_1$ on the minority Aggressive class. Unsupervised K-means clustering of the same PI features naturally separates the data into three behavioral clusters whose ANOVA-verified risk profiles align with the MOR-defined classes, confirming the behavioral relevance of the topological descriptors. These results provide empirical evidence that PI features capture safety-critical structure more effectively than raw kinematics and demonstrate the robustness and scalability of TDA for analyzing large, noisy datasets. The proposed approach shows strong potential for real-time driver monitoring, risk assessment, and data-driven transportation management, with implications for traffic safety, autonomous systems, and personalized insurance.