Публикация:Gorban (2008), Principal Manifolds

Материал из MachineLearning.

Версия 14:18, 26 сентября 2009

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

 @book{NPCA2007,
   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
 }

Аннотация

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.

Contents

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

Ссылки

• Нелинейный метод главных компонент
• Principal Manifolds for Data Visualization and Dimension Reduction