Professor Jochen Einbeck jochen.einbeck@durham.ac.uk
Professor
Representing complex data using localized principal components with application to astronomical data.
Einbeck, Jochen; Evers, Ludger; Bailer-Jones, Coryn
Authors
Ludger Evers
Coryn Bailer-Jones
Contributors
A Gorban
Editor
B Kegl
Editor
D Wunsch
Editor
A Zinovyev
Editor
Abstract
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.
Citation
Einbeck, J., Evers, L., & Bailer-Jones, C. (2008). Representing complex data using localized principal components with application to astronomical data. In A. Gorban, B. Kegl, D. Wunsch, & A. Zinovyev (Eds.), Lecture Notes in Computational Science and Engineering (180-204). Springer Verlag. https://doi.org/10.1007/978-3-540-73750-6_7
Publication Date | 2008 |
---|---|
Publisher | Springer Verlag |
Pages | 180-204 |
Series Number | 58 |
Book Title | Lecture Notes in Computational Science and Engineering. |
Chapter Number | 7 |
ISBN | 9783540737490 |
DOI | https://doi.org/10.1007/978-3-540-73750-6_7 |
Keywords | Localized principal components, principal curves, dimension reduction, Gaia |
Public URL | https://durham-repository.worktribe.com/output/1688098 |
Publisher URL | http://www.springerlink.com/content/n4607j221677x08x/ |
Additional Information | Also available on arXiv: http://arxiv.org/abs/0709.1538 |
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