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, PM2.5, 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.
Landfill leachate, a major environmental contaminant, is influenced by multiple factors and can migrate through landfill systems, spreading over considerable distances and polluting surrounding ecosystems. This study utilized Ball Mapper, a topological data analysis tool, to qualitatively explore hidden relationships between physicochemical parameters in leachate, surface water, and the baseliner, which can aid in pollution monitoring. The resulting Ball Mapper topological graphs uncovered behavioral similarities and relationships among parameters across different seasonal conditions. The analysis effectively revealed underlying patterns and interconnections by clustering parameters with similar behavior into the same nodes and linking those with hidden similarities. Additionally, Spearman correlation was used to validate the Ball Mapper output, the analysis showed that baseliner and surface water had a weak linear relationship with leachate, except for PO₄3 (r = 0.99), SO₄2⁻(r = 0.71), TSS (r = 0.82), and pH (r = 0.95) in surface water across seasons, which could be as a result of runoff, sediment transport, and environmental factors rather than direct leachate infiltration. The study also demonstrated that while seasonal variations in precipitation influenced leachate volume and pollutant concentrations, the landfill's engineered barriers effectively mitigated the potential environmental impact of leachate migration. Ball Mapper successfully showed the hidden behavior that traditional clustering methods may miss, highlighting its potential as a valuable tool for environmental monitoring.