🍩 Database of Original & Non-Theoretical Uses of Topology

1. Topological Data Analysis for Aviation Applications (2019)

   Max Z. Li, Megan S. Ryerson, Hamsa Balakrishnan

   Abstract

   Aviation data sets are increasingly high-dimensional and sparse. Consequently, the underlying features and interactions are not easily uncovered by traditional data analysis methods. Recent advancements in applied mathematics introduce topological methods, offering a new approach to obtain these features. This paper applies the fundamental notions underlying topological data analysis and persistent homology (TDA/PH) to aviation data analytics. We review past aviation research that leverage topological methods, and present a new computational case study exploring the topology of airport surface connectivity. In each case, we connect abstract topological features with real-world processes in aviation, and highlight potential operational and managerial insights.

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   • Airline networks
   • Aviation
   • Persistent homology