Optimal Riemannian quantization with an application to air traffic analysis

Alice Le Brigant (1) , Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

The goal of optimal quantization is to find the best approximation of a probability distribution by a discrete measure with finite support. In this paper, we introduce an algorithm that computes the optimal finite approximation when the probability distribution is defined over a complete Riemannian manifold. It is a natural extension of the well-known Competitive Learning Vector Quantization algorithm. We use it to analyze air traffic complexity in air traffic management (ATM). From a given air traffic situation, we extract an image of covariance matrices and use CLRQ (Competitive Learning Riemannian Quantization) to find the best finite approximation of their empirical spatial distribution. This yields a digest of the traffic as well as a clustering of the airspace into zones that are homogeneous with respect to complexity. These digests can then be compared using discrete optimal transport and be further used as inputs of a machine learning algorithm or as indexes in a traffic database.

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

Alice Le Brigant, Stéphane Puechmorel. Optimal Riemannian quantization with an application to air traffic analysis. 2018. ⟨hal-01816865v1⟩