Functional Principal Component Analysis via Regularized Basis Expansion and Its Application

Recently, functional data analysis (FDA) has received considerable attention in various fields and a number of successful applications have been reported (see, e.g., Ramsay and Silverman (2005)). The basic idea behind FDA is the expression of discrete observations in the form of a function and the drawing of information from a collection of functional data by applying concepts from multivariate data analysis. There are some reports discussing principal component analysis for functional data. We introduce the regularized functional principal component analysis for multi-dimensional functional data set, using Gaussian radial basis functions. The use of the proposed method is illustrated through the analysis of the three-dimensional (3D) protein structural data by converting the 3D protein data to the 3-dimensional functional data set. The visual inspection showed that the PC (principal component) plot mostly coincided with the biological classification.