Principal Manifolds for Data Visualization and Dimension Reduction

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Alexander N. Gorban, Balázs Kégl, Donald C. Wunsch, Andrei Zinovyev
Springer Science & Business Media, 2007 - Computers - 334 pages

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.

 

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Contents

Contents
1
References
39
References
65
References
91
References
127
The Iterative Extraction Approach to Clustering
151
References
174
Components
192
Principal Trees
219
of Bacterial Genomes
229
Diffusion Maps a Probabilistic Interpretation for Spectral
238
On Bounds for Diffusion Discrepancy and Fill Distance
261
References
269
Dimensionality Reduction and Microarray Data
293
References
307
PCA and KMeans Decipher Genome
309

References
199
References
216
Color Plates
325
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