  We encounter a bottleneck when we try to borrow the strength of classical
classifiers to classify functional data. The major issue is that functional
data are intrinsically infinite dimensional, thus classical classifiers cannot
be applied directly or have poor performance due to the curse of
dimensionality. To address this concern, we propose to project functional data
onto one specific direction, and then a distance-weighted discrimination DWD
classifier is built upon the projection score. The projection direction is
identified through minimizing an empirical risk function that contains the
particular loss function in a DWD classifier, over a reproducing kernel Hilbert
space. Hence our proposed classifier can avoid overfitting and enjoy appealing
properties of DWD classifiers. This framework is further extended to
accommodate functional data classification problems where scalar covariates are
involved. In contrast to previous work, we establish a non-asymptotic
estimation error bound on the relative misclassification rate. In finite sample
case, we demonstrate that the proposed classifiers compare favorably with some
commonly used functional classifiers in terms of prediction accuracy through
simulation studies and a real-world application.
