A covariate adjusted subspace projected functional data classification (SPFC) method is proposed
for curves or functional data classification with accommodating additional covariate information.
Based on the framework of subspace projected functional data clustering, curves of each cluster are
embedded in the cluster subspace spanned by a mean function and eigenfunctions of the covariance
kernel. We assume that the mean function may depend on covariates, and curves of each cluster
are represented by the covariate adjusted functional principal components analysis (FPCA) model or
covariate adjusted Karhunen-Loève expansion. Under the assumption that all the groups have different
mean functions and eigenspaces, an observed curve is classified into the best predicted class by
minimizing the distance between the observed curve and predicted functions via subspace projection
among all clusters based on the covariate adjusted FPCA model. The proposed covariate adjusted
SPFC method that accommodates additional information of other covariates is advantageous to improving
the classification error rate. Numerical performance of the proposed method is examined by
simulation studies, with an application to a data example.
