Principal curves of oriented points: theoretical and computational improvements
The authors studied the principal curves, i.e., functional extensions of principal components, and presented further the development of the first author's previous work [J. Multivariate Anal. 77, No. 1, 84--116 (2001; Zbl 1033.62048)]), where principal curves of oriented points (PCOP) were defined. The present paper extends this approach in two directions. First, a bandwidth choice method for the smoother used in the PCOP construction is given. This choice is based on a Minimum Spaning Tree previously computed, that also helps to detect clusters in PCOP intermediate steps. Secondly, a flexible object oriented application of the PCOP method, allowing to manage data of any dimension and to extract systems of curves of any order, is presented. The design is recursive, as well as the general definition of PCOP. Examples on synthetic and real data are included and discussed.
scientific article; zbMATH DE number 2118515