Spatial depth-based classification for functional data

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.

Detecting a structural change in functional time series using local Wilcoxon statistic

“…Sguera et al (2016); Nagy et al (2016). The conducted simulation studies as well as the studied empirical examples show a big potential of our proposal in a context of discrimination between the alternatives and in a a consequence in detecting a structural change.…”

Resampling-based Classification Using Depth for Functional Curves

“…Subsequently, the performance needs to be studied with the random projection depth types (4; 2). In addition, the paper adopts a weighted distance metric according to inverse variance weighting, but WMD can be a good candidate for practice as it has been reported (23) to have an overall better performance compared to WAD. …”

“…Fraiman and Muniz's depth (FM depth) (9) is defined as an integrated value of simplicial depths (12; 13) which are calculated with the values of a function over the whole interval (9). Since FM depth, some functional depths have been proposed, such as h-mode depth (3), Graphical Band based Depth (GBD) (14) and Kernelized Functional Spatial Depth (KFSD) (23). In addition to these, there is also a random projection type.…”

“…However, DTM uses an Euclidean distance metric while WAD uses a weighted distance metric. In addition, Within Maximu Depth (WMD) was proposed (23). WMD compares depths of an object with respect to each class and assigns the object to the ACCEPTED MANUSCRIPT class for which the depth value is higher.…”

Local half-region depth for functional data

“…Another application of the local modified half-region depth is available in Agostinelli and Rotondi [2015] where the analysis of the shape of macroseismic fields is performed by the local modified half-region depth. Sguera et al [2014] proposes another functional depth which is local-oriented and kernel-based version of the functional spatial depth Chakraborty and Chaudhuri [2014].…”