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Principal Manifolds for Data Visualization and Dimension Reduction

  • Conference proceedings
  • © 2008

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Editors:
  1. Alexander N. Gorban

    1. University of Leicester, Leicester, UK

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  2. Balázs Kégl

    1. University of Paris-Sud - CNRS, Orsay, France

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  3. Donald C. Wunsch

    1. University of Missouri - Rolla, Rolla, USA

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  4. Andrei Y. Zinovyev

    1. Institut Curie Service Bioinformatique, Paris, France

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

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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.

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Table of contents (14 papers)

  1. Front Matter

    Pages I-XXIII
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  2. Developments and Applications of Nonlinear Principal Component Analysis – a Review

    • Uwe Kruger, Junping Zhang, Lei Xie
    Pages 1-43

  3. Nonlinear Principal Component Analysis: Neural Network Models and Applications

    • Matthias Scholz, Martin Fraunholz, Joachim Selbig
    Pages 44-67

  4. Learning Nonlinear Principal Manifolds by Self-Organising Maps

    • Hujun Yin
    Pages 68-95

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

    • Alexander N. Gorban, Andrei Y. Zinovyev
    Pages 96-130

  6. Topology-Preserving Mappings for Data Visualisation

    • Marian Pena, Wesam Barbakh, Colin Fyfe
    Pages 131-150

  7. The Iterative Extraction Approach to Clustering

    • Boris Mirkin
    Pages 151-177

  8. Representing Complex Data Using Localized Principal Components with Application to Astronomical Data

    • Jochen Einbeck, Ludger Evers, Coryn Bailer-Jones
    Pages 178-201

  9. Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit

    • Stéphane Girard, Serge Iovleff
    Pages 202-218

  10. Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes

    • Alexander N. Gorban, Neil R. Sumner, Andrei Y. Zinovyev
    Pages 219-237

  11. Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms

    • Boaz Nadler, Stephane Lafon, Ronald Coifman, Ioannis G. Kevrekidis
    Pages 238-260

  12. On Bounds for Diffusion, Discrepancy and Fill Distance Metrics

    • Steven B. Damelin
    Pages 261-270

  13. Geometric Optimization Methods for the Analysis of Gene Expression Data

    • Michel Journée, Andrew E. Teschendorff, Pierre-Antoine Absil, Simon Tavaré, Rodolphe Sepulchre
    Pages 271-292

  14. Dimensionality Reduction and Microarray Data

    • David A. Elizondo, Benjamin N. Passow, Ralph Birkenhead, Andreas Huemer
    Pages 293-308

  15. PCA and K-Means Decipher Genome

    • Alexander N. Gorban, Andrei Y. Zinovyev
    Pages 309-323

  16. Back Matter

    Pages 325-334
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Editors and Affiliations

  • University of Leicester, Leicester, UK

    Alexander N. Gorban

  • University of Paris-Sud - CNRS, Orsay, France

    Balázs Kégl

  • University of Missouri - Rolla, Rolla, USA

    Donald C. Wunsch

  • Institut Curie Service Bioinformatique, Paris, France

    Andrei Y. Zinovyev

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