Functional data classification using covariate-adjusted subspace projection

Pai-Ling Li

Department of Statistics

Tamkang University

plli@gms.tku.edu.tw

We propose a covariate-adjusted subspace projection method for classifying functional data, where the covariate effects on the response functions influence the classification outcome. The proposed method is a subspace classifier based on functional projection, and the covariates affect the response function through the mean of a functional regression model. We assume that the response functions in each class are embedded in a class specific subspace spanned by a covariate-adjusted mean function and a set of eigenfunctions of the covariance kernel through the covariate-adjusted Karhunen-Loève expansion. A newly observed response function is classified into the optimally predicted class that has the minimal distance between the observation and its projection onto the subspaces among all classes. The covariate adjustment is useful for functional classification, especially when the covariate effects on the mean functions are significantly different among the classes. Numerical performance of the proposed method is demonstrated by simulation studies, with an application to a data example. This is a joint work with Jeng-Min Chiou and Yu Shyr.Keyword: classification, discriminant analysis, functional data analysis, functional principal component analysis