Topological Data Analysis in Air Traffic Management: the shape of big flight data sets

TL;DR

The paper addresses the challenge of extracting meaningful structure from high-dimensional air traffic trajectory data. It adopts Topological Data Analysis, specifically Vietoris–Rips filtrations and persistence landscapes, to generate airport-specific footprints and compare them to conventional classifications. The study demonstrates a proof-of-concept on Spain's Summer 2018 airport data, showing that topology-based footprints can reveal grouping, geographic patterns, and anomalies, and it compares TDA-derived classifications with centrality-based approaches. The findings suggest that combining TDA with traditional network metrics can enhance airport classification, anomaly detection, and decision-support in ATM, offering a path toward more data-driven and robust analyses in aviation systems.

Abstract

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.

Figures (10)

• Figure 1: Persistence Diagram and Barcode of $H_0$ and $H_1$ for 150 random points on $\mathbb{S}^2\subset\mathbb{R}^3$. Regarding the left figure, the x-axis represents the birth and the y-axis the death of each topological feature. Regarding the right figure, the x-axis represents the birth and the death of each topological feature.
• Figure 2: On the left: $PD_0$ and $PD_1$ of $10$ points on $\mathbb{S}^2\subset\mathbb{R}^3$. On the center: the landscapes of the $H_0$. On the right: the landscapes of the $H_1$.
• Figure 3: On the left and center: landscape number $4$ and $69$ respectively of the sphere experiment. On the right: the average landscape.
• Figure 4: On the top left: The planned trajectory for a Bilbao-Lisbon flight on the 21st July 2019. On the top right: The real trajectory the plane followed. At the bottom: Both trajectories displayed con the same map.
• Figure 5: Point cloud of Santander's airport on the 29th June 2019.

Theorems & Definitions (6)

• Remark
• Remark
• Remark
• Remark
• Remark
• Remark