Abstract
In this paper, we deal with functional principal points of Gaussian random functions and functional clustering. The k principal points of a p-variate random variable X are defined as the k points which minimize the expected squared distance of X from the nearest of the point (Flury, 1990). The concept of principal points can be extended to functional data analysis (Tarpey & Kinateder, 2003), and we call the extended principal points functional principal points. Functional principal points of random functions have a close relation to functional cluster analysis. We derive functional principal points of polynomial random functions using orthogonal basis expansion. For functional data according to Gaussian random functions, we discuss the relation between the optimum clustering of the functional data and the functional principal points. We also investigate the number of local minima of the functional clustering algorithm with numerical experiments.
