Functional data classification: a wavelet approach

In recent years, several methods have been proposed to deal with functional data classification problems (e.g., one-dimensional curves or two- or three-dimensional images). One popular general approach is based on the kernel-based method, proposed by Ferraty and Vieu (Comput Stat Data Anal 44:161-173, 2003). The performance of this general method depends heavily on the choice of the semi-metric. Motivated by Fan and Lin (J Am Stat Assoc 93:1007-1021, 1998) and our image data, we propose a new semi-metric, based on wavelet thresholding for classifying functional data. This wavelet-thresholding semi-metric is able to adapt to the smoothness of the data and provides for particularly good classification when data features are localized and/or sparse. We conduct simulation studies to compare our proposed method with several functional classification methods and study the relative performance of the methods for classifying positron emission tomography images.