Information Geometry for Safety Data Processing

Florence Nicol (1) , Stéphane Puechmorel (2)

1 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
2 ENAC - Ecole Nationale de l'Aviation Civile

Air traffic system generates huge amounts of data, most of them being only partly exploited. One important issue is the functional nature of the samples that consist mainly in curves. Analyzing this kind of highly structured data requires dedicated tools. Most of the time, the functions considered are expanded on a truncated Hilbert basis then usual multivariate statistics tools are applied on them. When additional constraints are put on the curves, like in applications related to air traffic where operational considerations are to be taken into account, this approach is no longer applicable. The present article surveys some recent results obtained by the authors using a new framework where curves are represented as regularized currents. The question of high dimensional data with intrinsic redundancy is also discussed and a possible extension of the already obtained results is sketched.

Mots clés: curve clustering; probability distribution estimation; functional statistics; safety data analysis

Domaines: Géométrie différentielle [math.DG]

Florence Nicol, Stéphane Puechmorel. Information Geometry for Safety Data Processing. AEGATS ‘16, Advanced Aircraft Efficiency in a Global Air Transport System, AAF, Apr 2016, Paris, France. ⟨hal-01305791⟩