Curves Similarity Based on Higher Order Derivatives

Florence Nicol (1) , Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

In many applications, data originate from the observation of a phenomenon depending on time. Trajectories of mobiles fall within this category and receive an increasing attention as many connected objects have the ability to broadcast their positions. When the raw location is the value of interest, several statistical procedures exist to deal with analysis of trajectories. Depending on whether the geometrical shape or the time to position relation is relevant, one will use a parametrization invariant distance or a simple L 2 metric to assess the similarity between any two trajectories. However, it is sometimes advisable to use higher order information like velocity or acceleration, while retaining some kind of geometrical invariance. The purpose of the present work is to introduce a framework especially adapted to such a situation.

Mots clés: bundle metric; curve manifold; Shape space

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

Florence Nicol, Stéphane Puechmorel. Curves Similarity Based on Higher Order Derivatives. ALLDATA 2017, The Third International Conference on Big Data, Small Data, Linked Data and Open Data, Apr 2017, Venice, Italy. pp.3-8/ISBN: 978-1-61208-552-4. ⟨hal-01799109⟩