Spatial depth-based classification for functional data

Carlo Sguera, Pedro Galeano and Rosa Elvira Lillo Rodríguez

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: 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.

Keywords: Depth; notion; Spatial; functional; depth; Supervised; functional; classification; Depth-based; method; Outliers (search for similar items in EconPapers)
Date: 2012-05
New Economics Papers: this item is included in nep-ecm and nep-ure
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Citations: View citations in EconPapers (1)

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Journal Article: Spatial depth-based classification for functional data (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws120906

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