Introduction to Multivariate Analysis: Linear and Nonlinear Modeling

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