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Local Principal Curves

Einbeck, Jochen; Tutz, Gerhard; Evers, Ludger

Authors

Gerhard Tutz

Ludger Evers



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.
Publisher URL http://www.ingentaconnect.com/content/klu/stco/2005/00000015/00000004/00004073


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