Another Look at Principal Curves and Surfaces
Principal curves have been defined as smooth curves passing through the "middle" of a multidimensional data set. They are nonlinear generalizations of the first principal component, a characterization of which is the basis of the definition of principal curves. We establish a new characterization of the first principal component and base our new definition of a principal curve on this property. We introduce the notion of principal oriented points and we prove the existence of principal curves passing through these points. We extend the definition of principal curves to multivariate data sets and propose an algorithm to find them. The new notions lead us to generalize the definition of total variance. Successive principal curves are recursively defined from this generalization. The new methods are illustrated on simulated and real data sets.
Volume (Year): 77 (2001)
Issue (Month): 1 (April)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jamshid Etezadi-Amoli & Roderick McDonald, 1983. "A second generation nonlinear factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 315-342, September.
- Victor Yohai & Werner Ackermann & Cristina Haigh, 1985. "Nonlinear principal components," Quality & Quantity: International Journal of Methodology, Springer, vol. 19(1), pages 53-69, January.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:77:y:2001:i:1:p:84-116. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If references are entirely missing, you can add them using this form.