Local principal curves

Einbeck, J., Tutz, G. and Evers, L. (2005) Local principal curves. Statistics and Computing, 15(4), pp. 301-313. (doi: 10.1007/s11222-005-4073-8)

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 curveswhich may ormay 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.

• Item Type: Articles
• Additional Information: The original publication is available at www.springerlink.com
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Evers, Dr Ludger
• Authors: Einbeck, J., Tutz, G., and Evers, L.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Statistics and Computing
• Publisher: Springer
• ISSN: 0960-3174
• Copyright Holders: Copyright © 2005 Springer
• First Published: First published in Statistics and Computing 15(4):301-313
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher