Continuum centroid classifier for functional data

For the binary classification of functional data, we propose the continuum centroid classifier (CCC), which is constructed by projecting the functional data onto one specific direction. This direction is obtained via bridging the regression and classification. Our technique is neither unsupervised nor fully supervised; instead, we control the extent of the supervision. Thanks to the intrinsic infinite dimension of functional data, one of the two subtypes of CCC enjoys an (asymptotic) zero misclassification rate. Our approach includes an effective algorithm that yields a consistent empirical classifier. Simulation studies demonstrate the competitive performance of the CCC in different scenarios. Finally, we apply the CCC to two real examples.