Principal Manifolds for Data Visualization and Dimension Reduction
Editor(s)
Gorban, Alexander N. and Kégl, Balázs and Wunsch, Donald C. and Zinovyev, Andrei Y.
Abstract
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.
Recommended Citation
U. Kruger et al., "Principal Manifolds for Data Visualization and Dimension Reduction," Lecture Notes in Computational Science and Engineering, vol. 58, pp. 1 - 340, Springer Verlag (Germany), Jan 2007.
The definitive version is available at https://doi.org/10.1007/978-3-540-73750-6
Department(s)
Electrical and Computer Engineering
International Standard Book Number (ISBN)
978-3540737490
International Standard Serial Number (ISSN)
1439-7358
Document Type
Book
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2007 Springer Verlag (Germany), All rights reserved.
Publication Date
01 Jan 2007
