Spatial depth-based classification for functional data
AbstractFunctional data are becoming increasingly available and tractable because of the last technological advances. We enlarge the number of functional depths by defining two new depth functions for curves. Both depths are based on a spatial approach: the functional spatial depth (FSD), that shows an interesting connection with the functional extension of the notion of spatial quantiles, and the kernelized functional spatial depth (KFSD), which is useful for studying functional samples that require an analysis at a local level. Afterwards, we consider supervised functional classification problems, and in particular we focus on cases in which the samples may contain outlying curves. For these situations, some robust methods based on the use of functional depths are available. By means of a simulation study, we show how FSD and KFSD perform as depth functions for these depth-based methods. The results indicate that a spatial depthbased classification approach may result helpful when the datasets are contaminated, and that in general it is stable and satisfactory if compared with a benchmark procedure such as the functional k-nearest neighbor classifier. Finally, we also illustrate our approach with a real dataset.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws120906.
Date of creation: May 2012
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Depth notion; Spatial functional depth; Supervised functional classification; Depth-based method; Outliers;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-29 (All new papers)
- NEP-ECM-2012-05-29 (Econometrics)
- NEP-URE-2012-05-29 (Urban & Real Estate Economics)
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- Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
- Cuevas, Antonio & Fraiman, Ricardo, 2009. "On depth measures and dual statistics. A methodology for dealing with general data," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 753-766, April.
- Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
- Esdras Joseph & Pedro Galeano & Rosa E. Lillo, 2013. "The Mahalanobis distance for functional data with applications to classification," Statistics and Econometrics Working Papers ws131312, Universidad Carlos III, Departamento de Estadística y Econometría.
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