  Aiming at the binary classification of functional data, we propose the
continuum centroid classifier (CCC) built upon projections of functional data
onto one specific direction. This direction is obtained via bridging the
regression and classification. Controlling the extent of supervision, our
technique is neither unsupervised nor fully supervised. Thanks to the intrinsic
infinite dimension of functional data, one of two subtypes of CCC enjoys the
(asymptotic) zero misclassification rate. Our proposal includes an effective
algorithm that yields a consistent empirical counterpart of CCC. Simulation
studies demonstrate the performance of CCC in different scenarios. Finally, we
apply CCC to two real examples.
