Functional Principal Points and Functional Cluster Analysis

In this chapter, we deal with functional principal points and functional cluster analysis. The k principal points [4] are defined as the set of k points which minimizes the sum of expected squared distances from every points in the distribution to the nearest points of the set, and are mathematically equivalent to centers of gravity by k-means clustering [3]. The concept of principal points can be extended for functional data analysis [16]. We call the extended principal points functional principal points.