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Bioinformatics Advance Access published online on August 18, 2005
Bioinformatics, doi:10.1093/bioinformatics/bti634
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© The Author (2005). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org
Received January 5, 2005
Revised August 2, 2005
Accepted August 15, 2005

Article

Nonlinear PCA: a missing data approach

Matthias Scholz 1*, Fatma Kaplan 2, Charles L. Guy 2, Joachim Kopka 1, and Joachim Selbig 3

1 Max Planck Institute of Molecular Plant Physiology, Potsdam, Germany
2 University of Florida, Plant Molecular and Cellular Biology Program, Department of Environmental Horticulture, Gainesville, Florida 32611, USA
3 Max Planck Institute of Molecular Plant Physiology, Potsdam, Germany; University of Potsdam, Bioinformatics, Germany

* To whom correspondence should be addressed.
Matthias Scholz, E-mail: scholz{at}mpimp-golm.mpg.de


  Abstract

Motivation: Visualising and analysing the potential nonlinear structure of a data set is becoming an important task in molecular biology. This is even more challenging when the data have missing values.

Results: Here, we propose an inverse model that performs nonlinear principal component analysis (NLPCA) from incomplete data sets. Missing values are ignored while optimising the model, but can be estimated afterwards. Results are shown for both artificial and experimental data sets. In contrast to linear methods, nonlinear methods were able to give better missing value estimations for nonlinear structured data.

Application: We applied this technique to a time course of metabolite data from a cold stress experiment on the model plant Arabidopsis thaliana, and could approximate the mapping function from any time point to the metabolite responses. Thus, the inverse NLPCA provides greatly improved information for better understanding the complex response to cold stress.


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