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Nonlinear Principal Component Analysis: Neural Network Models and Applications

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Principal Manifolds for Data Visualization and Dimension Reduction

Part of the book series: Lecture Notes in Computational Science and Enginee ((LNCSE,volume 58))

Nonlinear principal component analysis (NLPCA) as a nonlinear generalisation of standard principal component analysis (PCA) means to generalise the principal components from straight lines to curves. This chapter aims to provide an extensive description of the autoassociative neural network approach for NLPCA. Several network architectures will be discussed including the hierarchical, the circular, and the inverse model with special emphasis to missing data. Results are shown from applications in the field of molecular biology. This includes metabolite data analysis of a cold stress experiment in the model plant Arabidopsis thaliana and gene expression analysis of the reproductive cycle of the malaria parasite Plasmodium falciparum within infected red blood cells.

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Author information

Authors and Affiliations

  1. Competence Centre for Functional Genomics, Institute for Microbiology, Ernst-Moritz-Arndt-University Greifswald, F.-L.-Jahn-Str. 15, 17487, Greifswald, Germany

    Matthias Scholz & Martin Fraunholz

  2. Institute for Biochemistry and Biology, University of Potsdam, Am Mühlenberg 1, 14424, Potsdam, Germany

    Joachim Selbig

Authors
  1. Matthias Scholz
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  2. Martin Fraunholz
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  3. Joachim Selbig
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Editor information

Editors and Affiliations

  1. University of Leicester, University Road, LE1 7RH, Leicester, UK

    Alexander N. Gorban

  2. University of Paris-Sud - CNRS, Bâtiment 2000, 91898, Orsay, France

    Balázs Kégl

  3. University of Missouri - Rolla, 1870 Miner Circle, 65409, Rolla, MO, USA

    Donald C. Wunsch

  4. Institut Curie Service Bioinformatique, rue d'Ulm 26, 75248, Paris, France

    Andrei Y. Zinovyev

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Scholz, M., Fraunholz, M., Selbig, J. (2008). Nonlinear Principal Component Analysis: Neural Network Models and Applications. In: Gorban, A.N., Kégl, B., Wunsch, D.C., Zinovyev, A.Y. (eds) Principal Manifolds for Data Visualization and Dimension Reduction. Lecture Notes in Computational Science and Enginee, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73750-6_2

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