Principal Manifolds for Data Visualization and Dimension Reduction (Lecture Notes in Computational Science and Engineering 58)

Alexander N. Gorban, Balazs Kegl, Donald C. Wunsch, Andrei Zinovyev

ISBN 10: 3540737499 / ISBN 13: 9783540737490

Published by Springer, 2007

About this Item

340 pp., paperback, fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

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Bibliographic Details

• Title: Principal Manifolds for Data Visualization and Dimension Reduction (Lecture Notes in Computational Science and Engineering 58)
• Publisher: Springer
• Publication Date: 2007
• Language: English
• ISBN 10: 3540737499
• ISBN 13: 9783540737490
• Binding: Soft cover
• Condition: Fine

About this title

Synopsis

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.