Spatial depth-based classification for functional data Articles uri icon

published in

publication date

  • December 2014

start page

  • 725

end page

  • 750

issue

  • 4

volume

  • 23

international standard serial number (ISSN)

  • 1133-0686

electronic international standard serial number (EISSN)

  • 1863-8260

abstract

  • We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful for studying functional samples that require an analysis at a local level. In addition, we consider supervised functional classification problems, focusing on cases in which the differences between groups are not extremely clear-cut or the data may contain outlying curves. We perform classification by means of some available robust methods that involve the use of a given functional depth, including FSD and KFSD, among others. We use the functional k-nearest neighbor classifier as a benchmark procedure. The results of a simulation study indicate that the KFSD-based classification approach leads to good results. Finally, we consider two real classification problems, obtaining results that are consistent with the findings observed with simulated curves.

keywords

  • functional depths; functional outliers; functional spatial depth; kernelized functional spatial depth; supervised functional classification; discriminant-analysis; curves; regression; notions; spaces