Topological data analysis in air traffic management: The shape of big flight data sets

Analyzing flight trajectory data sets poses challenges due to the intricate interconnections among various factors and the high dimensionality of the data. Topological Data Analysis (TDA) is a way of analyzing big data sets focusing on the topological features this data sets have as point clouds in some metric space. Techniques as the ones that TDA provides are suitable for dealing with high dimensionality and intricate interconnections. This paper introduces TDA and its tools and methods as a way to derive meaningful insights from ATM data. Our focus is on employing TDA to extract valuable information related to airports. Specifically, by utilizing persistence landscapes (a potent TDA tool) we generate footprints for each airport. These footprints, obtained by averaging over a specific time period, are based on the deviation of trajectories and delays. We apply this method to the set of Spanish' airports in the Summer Season of 2018. Remarkably, our results align with the established Spanish airport classification and raise intriguing questions for further exploration. This analysis serves as a proof of concept, showcasing the potential application of TDA in the ATM field. While previous works have outlined the general applicability of TDA in aviation, this paper marks the first comprehensive application of TDA to a substantial volume of ATM data. Finally, we present conclusions and guidelines to address future challenges in the ATM domain.