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Lecture Notes in Computational Science and Engineering

Principal Manifolds for Data Visualization and Dimension Reduction

Editors: Gorban, A.N., Kégl, B., Wunsch, D.C., Zinovyev, A. (Eds.)

  • New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described
  • Presentation of algorithms is supplemented by case studies
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eBook $149.00
price for USA (gross)
valid through October 16, 2017
  • ISBN 978-3-540-73750-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $189.00
price for USA
valid through October 16, 2017
  • ISBN 978-3-540-73749-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

In 1901, Karl Pearson invented Principal Component Analysis (PCA). Since then, PCA serves as a prototype for many other tools of data analysis, visualization and dimension reduction: Independent Component Analysis (ICA), Multidimensional Scaling (MDS), Nonlinear PCA (NLPCA), Self Organizing Maps (SOM), etc. The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described as well. Presentation of algorithms is supplemented by case studies, from engineering to astronomy, but mostly of biological data: analysis of microarray and metabolite data. The volume ends with a tutorial "PCA and K-means decipher genome". The book is meant to be useful for practitioners in applied data analysis in life sciences, engineering, physics and chemistry; it will also be valuable to PhD students and researchers in computer sciences, applied mathematics and statistics.

Table of contents (14 chapters)

  • Developments and Applications of Nonlinear Principal Component Analysis – a Review

    Kruger, Uwe (et al.)

    Pages 1-43

  • Nonlinear Principal Component Analysis: Neural Network Models and Applications

    Scholz, Matthias (et al.)

    Pages 44-67

  • Learning Nonlinear Principal Manifolds by Self-Organising Maps

    Yin, Hujun

    Pages 68-95

  • Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization

    Gorban, Alexander N. (et al.)

    Pages 96-130

  • Topology-Preserving Mappings for Data Visualisation

    Pena, Marian (et al.)

    Pages 131-150

Buy this book

eBook $149.00
price for USA (gross)
valid through October 16, 2017
  • ISBN 978-3-540-73750-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $189.00
price for USA
valid through October 16, 2017
  • ISBN 978-3-540-73749-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Principal Manifolds for Data Visualization and Dimension Reduction
Editors
  • Alexander N. Gorban
  • Balázs Kégl
  • Donald C. Wunsch
  • Andrei Zinovyev
Series Title
Lecture Notes in Computational Science and Engineering
Series Volume
58
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-73750-6
DOI
10.1007/978-3-540-73750-6
Softcover ISBN
978-3-540-73749-0
Series ISSN
1439-7358
Edition Number
1
Number of Pages
XXIV, 340
Number of Illustrations and Tables
68 b/w illustrations, 14 illustrations in colour
Topics