Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning

Alan J. Izenman (auth.)0-387-75958-6

Remarkable advances in computation and data storage and the ready availability of huge data sets have been the keys to the growth of the new disciplines of data mining and machine learning, while the enormous success of the Human Genome Project has opened up the field of bioinformatics.

These exciting developments, which led to the introduction of many innovative statistical tools for high-dimensional data analysis, are described here in detail. The author takes a broad perspective; for the first time in a book on multivariate analysis, nonlinear methods are discussed in detail as well as linear methods. 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 component analysis, support vector machines, and classification and regression trees. Another unique feature of this book is the discussion of database management systems.

This book is appropriate 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 in the book, over 200 exercises, and many color illustrations and photographs.

Alan J. Izenman is Professor of Statistics and Director of the Center for Statistical and Information Science at Temple University. He has also been on the faculties of Tel-Aviv University and Colorado State University, and has held visiting appointments at the University of Chicago, the University of Minnesota, Stanford University, and the University of Edinburgh. He served as Program Director of Statistics and Probability at the National Science Foundation and was Program Chair of the 2007 Interface Symposium on Computer Science and Statistics with conference theme of Systems Biology. He is a Fellow of the American Statistical Association.

Table of contents :
Front Matter….Pages i-xxv
Introduction and Preview….Pages 1-16
Data and Databases….Pages 17-44
Random Vectors and Matrices….Pages 45-74
Nonparametric Density Estimation….Pages 75-106
Model Assessment and Selection in Multiple Regression….Pages 107-158
Multivariate Regression….Pages 159-194
Linear Dimensionality Reduction….Pages 195-236
Linear Discriminant Analysis….Pages 237-280
Recursive Partitioning and Tree-Based Methods….Pages 281-314
Artificial Neural Networks….Pages 315-368
Support Vector Machines….Pages 369-406
Cluster Analysis….Pages 407-462
Multidimensional Scaling and Distance Geometry….Pages 463-504
Committee Machines….Pages 505-550
Latent Variable Models for Blind Source Separation….Pages 551-596
Nonlinear Dimensionality Reduction and Manifold Learning….Pages 597-632
Correspondence Analysis….Pages 633-666
Back Matter….Pages 667-733