Local Principal Curves

Einbeck, Jochen; Tutz, Gerhard; Evers, Ludger

Abstract

Principal components are a well established tool in dimension reduction. The extension to principal curves allows for general smooth curves which pass through the middle of a multidimensional data cloud. In this paper local principal curves are introduced, which are based on the localization of principal component analysis. The proposed algorithm is able to identify closed curves as well as multiple curves which may or may not be connected. For the evaluation of the performance of principal curves as tool for data reduction a measure of coverage is suggested. By use of simulated and real data sets the approach is compared to various alternative concepts of principal curves.

Citation

Einbeck, J., Tutz, G., & Evers, L. (2005). Local Principal Curves. Statistics and Computing, 15(4), 301-313. https://doi.org/10.1007/s11222-005-4073-8

• Journal Article Type: Article
• Publication Date: 2005-10
• Deposit Date: Jan 29, 2009
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Electronic ISSN: 1573-1375
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 15
• Issue: 4
• Pages: 301-313
• DOI: https://doi.org/10.1007/s11222-005-4073-8
• Keywords: Local smoothing, Mean shift, Principal components, Principal curves.
• Public URL: https://durham-repository.worktribe.com/output/1580155
• Publisher URL: http://www.ingentaconnect.com/content/klu/stco/2005/00000015/00000004/00004073