Functional principal component analysis of aircraft trajectories

Florence Nicol (1)

1 MAIAA-PROBA - Equipe MAIAA-PROBA

In Functional Data Analysis (FDA), the underlying structure of a raw observation is functional and data are assumed to be sample paths from a single stochastic process. Functional Principal Component Analysis (FPCA) generalizes the standard multivariate Principal Component Analysis (PCA) to the infinite-dimensional case by analyzing the covariance structure of functional data. By approximating infinite-dimensional random functions by a finite number of random score vectors, FPCA appears as a dimension reduction technique just as in the multivariate case and cuts down the complexity of data. This method is applied to aircraft trajectories and the problem of registration is discussed when phase and amplitude variations are mixed.

Mots clés: Functional Data Analysis; Principal Component Analysis; random variable; Karhunen-Loève decomposition; registration; dimension reduction

Domaines: Mathématiques [math]; Probabilités [math.PR]

Florence Nicol. Functional principal component analysis of aircraft trajectories. ISIATM 2013, 2nd International Conference on Interdisciplinary Science for Innovative Air Traffic Management, Jul 2013, Toulouse, France. ⟨hal-00867957⟩