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A robust algorithm for template curve estimation based on manifold embedding

Dimeglio, Chloé and Gallón, Santiago and Loubes, Jean-Michel and Maza, Elie A robust algorithm for template curve estimation based on manifold embedding. (2014) Computational Statistics & Data Analysis, 70. 373-386. ISSN 0167-9473

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Official URL: http://dx.doi.org/10.1016/j.csda.2013.09.030

Abstract

The problem of finding a template function that represents the common pattern of a sample of curves is considered. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. When the functional data lie on an unknown intrinsically low-dimensional smooth manifold, the corresponding empirical Fréchet median function is chosen as an intrinsic estimator of the template function. However, since the geodesic distance is unknown, it has to be estimated. For this, a version of the Isomap procedure is proposed, which has the advantage of being parameter free and easy to use. The feature estimated with this method appears to be a good pattern for the data, capturing the inner geometry of the curves. Comparisons with other methods, with both simulated and real datasets, are provided.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com/science/article/pii/S016794731300368X
Audience (journal):National peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
French research institutions > Institut National de la Recherche Agronomique - INRA (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universidad de Antioquia (COLOMBIA)
Laboratory name:
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Deposited By: Brigitte LAFFORGUE
Deposited On:17 Apr 2015 13:21

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