Using functional information for binary classifications
This paper addresses binary classification for continuous-time functional data. We propose a probabilistic binary classification (PBC) criterion grounded in inter-functional distances, along with a fully nonparametric estimation procedure. Unlike conventional paradigms relying on ordered scalar labels, PBC directly quantifies similarity between an individual’s trajectory and the functional mean of the positive group—bypassing structural assumptions or dimensionality reduction on functional biomarkers. The method integrates functional data analysis, nonparametric kernel estimation, and Monte Carlo simulation, implemented in R. Simulation studies and real-data analyses demonstrate that PBC exhibits strong robustness under moderate sample sizes and achieves significantly higher classification accuracy than state-of-the-art competitors—particularly in challenging settings involving high-dimensional, nonstationary, and small-sample functional biomarkers.