Публикация:Gorban (2008), Principal Manifolds

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Gorban, A.N., Kegl, B., Wunsch, D., Zinovyev, A.Y. Principal Manifolds for Data Visualisation and Dimension Reduction. — Springer, Berlin – Heidelberg – New York, 2008. — ISBN 978-3-540-73749-0

   author = "Gorban, A.N. and Kegl, B. and Wunsch, D. and Zinovyev, A.Y.",
   title = "Principal Manifolds for Data Visualisation and Dimension Reduction",
   publisher = "Springer, Berlin – Heidelberg – New York",
   year = "2008",
   url = "http://pca.narod.ru/contentsgkwz.htm",
   isbn = "978-3-540-73749-0",
   language = english



Первая в мировой научной литературе монография, посвященная методу главных многообразий (обобщения Кохоненовских SOM в том числе): Главные многообразия для визуализации и анализа данных, А. Горбань, Б. Кегль, Д. Вунш, А. Зиновьев (ред.), Шпрингер, 2007. Подготовлена международным коллективом авторов.


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 deciphers 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.

Written for: Researchers and graduate students


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

Uwe Kruger, Junping Zhang, Lei Xie

2 Nonlinear Principal Component Analysis: Neural Network Models and Applications

Matthias Scholz, Martin Fraunholz, Joachim Selbig

3 Learning Nonlinear Principal Manifolds by Self-Organising Maps

Hujun Yin

4 Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data visualization

Alexander N Gorban, Andrei Y Zinovyev

5 Topology-Preserving Mappings for Data Visualisation

Marian PeЇna, Wesam Barbakh, Colin Fyfe

6 The Iterative Extraction Approach to Clustering

Boris Mirkin

7 Representing Complex Data Using Localized Principal Components with Application to Astronomical Data

Jochen Einbeck, Ludger Evers, Coryn Bailer-Jones

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

Stґephane Girard, Serge Iovleff

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

Alexander N Gorban, Neil R Sumner, Andrei Y Zinovyev

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

Boaz Nadler, Stephane Lafon, Ronald Coifman, Ioannis G Kevrekidis

11 On Bounds for Diffusion, Discrepancy and Fill Distance Metrics

Steven B Damelin

12 Geometric Optimization Methods for the Analysis of Gene Expression Data

Michel Journґee, Andrew E Teschendorff, Pierre-Antoine Absil, Simon Tavarґe, Rodolphe Sepulchre

13 Dimensionality Reduction and Microarray data

David A Elizondo, Benjamin N Passow, Ralph Birkenhead, Andreas Huemer

14 PCA and K-Means Decipher Genome

Alexander N Gorban, Andrei Y Zinovyev


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