My Account Log in

1 option

Principal Manifolds for Data Visualization and Dimension Reduction / edited by Alexander N. Gorban, Balázs Kégl, Donald C. Wunsch, Andrei Zinovyev.

Ebook Central Academic Complete Available online

View online
Format:
Book
Contributor:
Gorbanʹ, A. N. (Aleksandr Nikolaevich)
Series:
Lecture Notes in Computational Science and Engineering, 2197-7100 ; 58
Language:
English
Subjects (All):
Automatic control.
Social sciences.
Humanities.
Mathematics--Data processing.
Mathematics.
Mathematical physics.
Computational intelligence.
Statistics.
Control and Systems Theory.
Humanities and Social Sciences.
Computational Science and Engineering.
Mathematical Methods in Physics.
Computational Intelligence.
Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
Local Subjects:
Control and Systems Theory.
Humanities and Social Sciences.
Computational Science and Engineering.
Mathematical Methods in Physics.
Computational Intelligence.
Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
Physical Description:
1 online resource (361 p.)
Edition:
1st ed. 2008.
Place of Publication:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Language Note:
English
Summary:
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.
Contents:
Developments and Applications of Nonlinear Principal Component Analysis – a Review
Nonlinear Principal Component Analysis: Neural Network Models and Applications
Learning Nonlinear Principal Manifolds by Self-Organising Maps
Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization
Topology-Preserving Mappings for Data Visualisation
The Iterative Extraction Approach to Clustering
Representing Complex Data Using Localized Principal Components with Application to Astronomical Data
Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit
Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes
Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms
On Bounds for Diffusion, Discrepancy and Fill Distance Metrics
Geometric Optimization Methods for the Analysis of Gene Expression Data
Dimensionality Reduction and Microarray Data
PCA and K-Means Decipher Genome.
Notes:
"This book is a collection of reviews and original papers presented partially at the workshop 'Principal manifolds for data cartography and dimension reduction' (Leicester, August 24-26, 2006)."--P. X.
Includes bibliographical references and index.
ISBN:
9786611070359
9781281070357
1281070351
9783540737506
3540737502
OCLC:
213093186

The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.

My Account

Shelf Request an item Bookmarks Fines and fees Settings

Guides

Using the Library Catalog Using Articles+ Library Account