  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 \textit{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.
