Constrained principal component analysis and related techniques (Q2864529)
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scientific article; zbMATH DE number 6232368
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constrained principal component analysis and related techniques |
scientific article; zbMATH DE number 6232368 |
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25 November 2013
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Mezzich's data
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food and cancer data
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Greenacre's data
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Tocher's data
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matrix operations
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projection matrices
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singular value decomposition
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constrained principal component analysis
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finer decompositions
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higher-order structures
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regularized constrained principal component analysis
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redundancy analysis
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canonical correlation analysis
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canonical discriminant analysis
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multidimensional scaling
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correspondence analysis
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constrained correspondence analysis
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nonsymmetric correspondence analysis
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multiple-set canonical correlation analysis
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multiple correspondence analysis
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vector preference models
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two-way CANDELINC
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growth curve models
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extended growth curve models
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seemingly unrelated regression
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Wedderburn-Guttman decomposition
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multilevel redundancy analysis
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weighted low rank approximations
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orthogonal Procrustes rotation
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image data matrices
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dimensionality selection
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reliability assessment
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missing data
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robust estimations
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data transformations
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biplot
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probabilistic principal component analysis
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algorithm
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additional constraints
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residual analysis
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graphical display of oblique components
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extended redundancy analysis
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generalized structured component analysis
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Constrained principal component analysis and related techniques (English)
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This book shows how constrained principal component analysis (CPCA) offers a unified framework for regression analysis and principal component analysis. The book has 6 chapters. Chapter 1 gives four concrete examples of CPCA that provide readers with a basic understanding of the technique and its applications. Chapter 2 gives a detailed account of two key mathematical ideas in CPCA: projection and singular value decomposition. Chapter 3 concentrates on CPCA, the main subject of this book, which gives the basic data requirements, models, and analytical tools for CPCA and their immediate extensions. Chapter 4 introduces techniques that are special cases of or closely related to CPCA including redundancy analysis, canonical correlation analysis, multidimensional scaling, correspondence analysis, etc.. Chapter 5 discusses several topics relevant to practical uses of CPCA including dimensionality selection, reliability assessment, missing data, etc.. Chapter 6 concludes with a chnique that imposes different constraints on different dimensions (DCDD), along with its analytical extensions. MATLAB(R) programs for CPCA and DCDD as well as data to create the book's examples are available on the author's website. This book can serve as a textbook for a graduate topics course. It can also be used as a reference book for faculty and professionals.
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