Principal curves of oriented points: theoretical and computational improvements
type: Item
instance of: scholarly article
title: Principal curves of oriented points: theoretical and computational improvements
zbMATH Open document ID: 1050.62064
author: Mario Huerta
author: Pedro Delicado
published in: Computational Statistics
publication date: 2004-11-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 62-08
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 90C90
zbMATH DE Number: 2118515
zbMATH Keywords: multidimensional data set
zbMATH Keywords: principal curves
zbMATH Keywords: clustering
zbMATH Keywords: smoothing
zbMATH Keywords: object oriented programming
zbMATH Keywords: minimum spanning tree
zbMATH Keywords: bandwidth choice population pyramids
describes a project that uses: GTM
describes a project that uses: KernSmooth
MaRDI profile type: Publication
full work available at URL: s001800300145
OpenAlex ID: W1594985570
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DOI: 10.1007/S001800300145
description: scientific article; zbMATH DE number 2118515