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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