Curve clustering based on second order information: application to bad runway condition detection

Florence Nicol (1) , Stéphane Puechmorel (1) , Baptiste Gregorutti (2) , Cindie Andrieu (2)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 Safety Line [Paris]

In air transportation, a huge amount of data is continuously recorded such as radar tracks that may be used for improving flight as well as airport safety. However, all known statistical algorithms, even those based on functional data, are unable to distinguish between a safety critical flight and another one departing from standard behavior, but otherwise safe. It is the case in airport safety when radar measurements are used for detecting incidents on airport surface. In this paper, we propose a change of paradigm by switching from a functional data framework to a geometrical one by representing curves as points in a shape manifold. In this way, any intrinsic structure of the data that is amenable to geometry can be directly encoded in the representation space. Based on an extension of a classical distance between shapes, a new one is defined, that explicitly takes into account the second derivative and can be related to slippery. Its properties are investigated in a first part, then some results on datasets of synthetic and real trajectories are presented.

Mots clés: curve clustering; outlier detection; similarity measure; shape; manifold; functional data analysis; air traffic management; airport safety; SRV metric

Domaines: Statistiques [math.ST]; Mathématiques [math]; Géométrie différentielle [math.DG]; Probabilités [math.PR]; Applications [stat.AP]; Méthodologie [stat.ME]

Florence Nicol, Stéphane Puechmorel, Baptiste Gregorutti, Cindie Andrieu. Curve clustering based on second order information: application to bad runway condition detection. 2023. ⟨hal-01799419v2⟩