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* Corresponding author 1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 GBF - Génomique et Biotechnologie des Fruits

Abstract : This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping Isomap algorithm is developed. Assuming that the functional data lie on an intrinsically low-dimensional smooth manifold with unknown underlying structure, we propose an approximation of the geodesic distance. This approximation is used to compute the corresponding empirical Fréchet median function, which provides an intrinsic estimator of the template function. Unlike the Isomap method, the algorithm has the advantage of being parameter free and easier to use. Comparisons with other methods, with both simulated and real datasets, show that the algorithm works well and outperforms these methods.

Keywords : Fréchet median functional data analysis Isomap

Author: Chloé Dimeglio - Santiago Gallón - Jean-Michel Loubes - Elie Maza -

Source: https://hal.archives-ouvertes.fr/


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