Principal curves of oriented points: Theoretical and computational improvements

Principal curves where introduced by Hastie & Stuetzle (1989) as smooth parametric curves passing through the middle of a multidimensional data set. Delicado (2001) defines Principal Curves of Oriented Points, based on the fixed points of a function from IRP into itself This definition is nonparametric and smoothing methods are used to find principal curves of a data set. Here we extend this work in two directions. First, we propose a bandwidth choice method based on the Minimum Spanning Tree of the data set. Second, we present an object oriented application that implements the principal curves computation for any dimension in a flexible recursive way. Examples on synthetic and real data are included.