Comparative analysis of Ball Mapper and conventional Mapper in investigating air pollutants' behavior

This study investigates the effectiveness and efficiency of two topological data analysis (TDA) techniques, the conventional Mapper (CM) and its variant version, the Ball Mapper (BM), in analyzing the behavior of six major air pollutants (NO₂, PM₁₀, PM_2.5, O₃, CO, and SO₂) across 60 air quality monitoring stations in Malaysia. Topological graphs produced by CM and BM reveal redundant monitoring stations and geographical relationships corresponding to air pollutant behavior, providing better visualization than traditional hierarchical clustering. Additionally, a comparative analysis of topological graph structures was conducted using node degree distribution, topological graph indices, and Dynamic Time Warping (DTW) to evaluate the sensitivity and performance of these TDA techniques. Both approaches yielded valuable insights in representing the air quality monitoring stations network; however, the complexity of CM, which requires multiple parameters, poses a challenge in graph construction. In contrast, the simplicity of BM, requiring only a single parameter, is preferable for representing air pollutant behavior. The findings suggest an alternative approach for assessing and identifying redundancies in air quality monitoring stations, which could contribute to improved air quality monitoring management and more effective regulatory policies.