Modern multivariate statistical techniques. Regression, classification, and manifold learning. (English) Zbl 1155.62040

Izenman, Alan Julian

Springer Texts in Statistics. New York, NY: Springer (ISBN 978-0-387-78188-4/hbk). xxv, 731 p. (2008).

New disciplines of data mining and machine learning are developed in the last time. The enormous success of the Human Genome Project has opened the field of bioinformatics. In this monograph, these exciting developments, which led to the introduction of many innovative statistical tools for high-dimensional data analysis, are described in detail. For the first time in a book on multivariate analysis, nonlinear as well as linear methods are discussed in detail. The techniques covered range from traditional multivariate methods, such as multiple regression, principal components, canonical variates, linear discriminant analysis, factor analysis, clustering, multidimensional scaling and correspondence analysis, to the newer methods of density estimation, projection pursuit, neural networks, multivariate reduced-rank regression, nonlinear manifold learning, bagging, boosting, random forests, independent components analysis, support vector machines, classification and regression trees. Another unique feature of this book is the discussion of database management systems.
This book is appropiate for advanced undergraduate students, graduate students, and researchers in statistics, computer science, artificial intelligence, psychology, cognitive sciences, business, medicine, bioinformatics and engineering. Familiarity with multivariable calculus, linear algebra and probability and statistics is required. The book presents a carefully-integrated mixture of theory and applications, and of classical and modern multivariate statistical techniques, including Bayesian methods. There are over 60 interesting data sets used as examples, over 200 exercises, and many colored illustrations and photographs.

Reviewer: T. Postelnicu (Bucureşti)

MSC:

62-02	Research exposition (monographs, survey articles) pertaining to statistics
62Hxx	Multivariate analysis
62G07	Density estimation
62M45	Neural nets and related approaches to inference from stochastic processes
68P15	Database theory
62G08	Nonparametric regression and quantile regression

Keywords:

discriminant analysis; cluster analysis; correspondence analysis