Principal Manifolds for Data Visualization and Dimension Reduction

  • Alexander N. Gorban
  • Balázs Kégl
  • Donald C. Wunsch
  • Andrei Y. Zinovyev
Conference proceedings

DOI: 10.1007/978-3-540-73750-6

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

Table of contents (14 papers)

  1. Front Matter
    Pages I-XXIII
  2. Nonlinear Principal Component Analysis: Neural Network Models and Applications
    Matthias Scholz, Martin Fraunholz, Joachim Selbig
    Pages 44-67
  3. Topology-Preserving Mappings for Data Visualisation
    Marian Pena, Wesam Barbakh, Colin Fyfe
    Pages 131-150
  4. 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
  5. Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms
    Boaz Nadler, Stephane Lafon, Ronald Coifman, Ioannis G. Kevrekidis
    Pages 238-260
  6. 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
  7. Dimensionality Reduction and Microarray Data
    David A. Elizondo, Benjamin N. Passow, Ralph Birkenhead, Andreas Huemer
    Pages 293-308
  8. PCA and K-Means Decipher Genome
    Alexander N. Gorban, Andrei Y. Zinovyev
    Pages 309-323
  9. Back Matter
    Pages 325-334

About these proceedings

Introduction

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.

Keywords

Analysis Clustering algorithm algorithms computer computer science data analysis linear optimization multidimensional scaling nonlinear optimization principal component analysis statistics visualization

Editors and affiliations

  • Alexander N. Gorban
    • 1
  • Balázs Kégl
    • 2
  • Donald C. Wunsch
    • 3
  • Andrei Y. Zinovyev
    • 4
  1. 1.University of LeicesterLeicesterUK
  2. 2.University of Paris-Sud - CNRSOrsayFrance
  3. 3.University of Missouri - RollaRollaUSA
  4. 4.Institut Curie Service BioinformatiqueParisFrance

Bibliographic information

  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-73749-0
  • Online ISBN 978-3-540-73750-6
  • Series Print ISSN 1439-7358