Spatial depth-based classification for functional data
Functional 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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- Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
- 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.
- LÃ³pez-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
- Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 10(2), pages 419-440, December.
- Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
- Anirvan Chakraborty & Probal Chaudhuri, 2014. "On data depth in infinite dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(2), pages 303-324, 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.
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