Select the Optimal Model for Interpreting Multivariate Data Introduction to Multivariate Analysis: Linear and Nonlinear Modeling shows how multivariate analysis is widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Along with the basic concepts of various procedures in traditional multivariate analysis, the book covers nonlinear techniques for clarifying phenomena behind observed multivariate data. It primarily focuses on regression modeling, classification and discrimination, dimension reduction, and clustering. The text thoroughly explains the concepts and derivations of the AIC, BIC, and related criteria and includes a wide range of practical examples of model selection and evaluation criteria. To estimate and evaluate models with a large number of predictor variables, the author presents regularization methods, including the L1 norm regularization that gives simultaneous model estimation and variable selection. For advanced undergraduate and graduate students in statistical science, this text provides a systematic description of both traditional and newer techniques in multivariate analysis and machine learning. It also introduces linear and nonlinear statistical modeling for researchers and practitioners in industrial and systems engineering, information science, life science, and other areas.
Introduction Regression Modeling Classification and Discrimination Dimension Reduction Clustering Linear Regression Models Relationship between Two Variables Relationships Involving Multiple Variables Regularization Nonlinear Regression Models Modeling Phenomena Modeling by Basis Functions Basis Expansions Regularization Logistic Regression Models Risk Prediction Models Multiple Risk Factor Models Nonlinear Logistic Regression Models Model Evaluation and Selection Criteria Based on Prediction Errors Information Criteria Bayesian Model Evaluation Criterion Discriminant Analysis Fisher's Linear Discriminant Analysis Classification Based on Mahalanobis Distance Variable Selection Canonical Discriminant Analysis Bayesian Classification Bayes' Theorem Classification with Gaussian Distributions Logistic Regression for Classification Support Vector Machines Separating Hyperplane Linearly Nonseparable Case From Linear to Nonlinear Principal Component Analysis Principal Components Image Compression and Decompression Singular Value Decomposition Kernel Principal Component Analysis Clustering Hierarchical Clustering Nonhierarchical Clustering Mixture Models for Clustering Appendix A: Bootstrap Methods Appendix B: Lagrange Multipliers Appendix C: EM Algorithm Bibliography Index
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