@article{ScholzKaplanGuyetal.2005,
  author    = {Scholz, Matthias and Kaplan, F. and Guy, C. L. and Kopka, Joachim and Selbig, Joachim},
  title     = {Non-linear PCA : a missing data approach},
  issn      = {1367-4803},
  year      = {2005},
  abstract  = {Motivation: Visualizing and analysing the potential non-linear structure of a dataset 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 non-linear principal component analysis (NLPCA) from incomplete datasets. Missing values are ignored while optimizing the model, but can be estimated afterwards. Results are shown for both artificial and experimental datasets. In contrast to linear methods, non-linear methods were able to give better missing value estimations for non-linear 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},
  language  = {en}
}
@phdthesis{Scholz2006,
  author    = {Scholz, Matthias},
  title     = {Approaches to analyse and interpret biological profile data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-7839},
  school      = {Universit{\"a}t Potsdam},
  year      = {2006},
  abstract  = {Advances in biotechnologies rapidly increase the number of molecules of a cell which can be observed simultaneously. This includes expression levels of thousands or ten-thousands of genes as well as concentration levels of metabolites or proteins. Such Profile data, observed at different times or at different experimental conditions (e.g., heat or dry stress), show how the biological experiment is reflected on the molecular level. This information is helpful to understand the molecular behaviour and to identify molecules or combination of molecules that characterise specific biological condition (e.g., disease). This work shows the potentials of component extraction algorithms to identify the major factors which influenced the observed data. This can be the expected experimental factors such as the time or temperature as well as unexpected factors such as technical artefacts or even unknown biological behaviour. Extracting components means to reduce the very high-dimensional data to a small set of new variables termed components. Each component is a combination of all original variables. The classical approach for that purpose is the principal component analysis (PCA). It is shown that, in contrast to PCA which maximises the variance only, modern approaches such as independent component analysis (ICA) are more suitable for analysing molecular data. The condition of independence between components of ICA fits more naturally our assumption of individual (independent) factors which influence the data. This higher potential of ICA is demonstrated by a crossing experiment of the model plant Arabidopsis thaliana (Thale Cress). The experimental factors could be well identified and, in addition, ICA could even detect a technical artefact. However, in continuously observations such as in time experiments, the data show, in general, a nonlinear distribution. To analyse such nonlinear data, a nonlinear extension of PCA is used. This nonlinear PCA (NLPCA) is based on a neural network algorithm. The algorithm is adapted to be applicable to incomplete molecular data sets. Thus, it provides also the ability to estimate the missing data. The potential of nonlinear PCA to identify nonlinear factors is demonstrated by a cold stress experiment of Arabidopsis thaliana. The results of component analysis can be used to build a molecular network model. Since it includes functional dependencies it is termed functional network. Applied to the cold stress data, it is shown that functional networks are appropriate to visualise biological processes and thereby reveals molecular dynamics.},
  subject      = {Bioinformatik},
  language  = {en}
}