Matrix-Based Introduction to Multivariate Data Analysis

This is the first textbook that allows readers who may be unfamiliar with matrices to understand a variety of multivariate analysis procedures in matrix forms. By explaining which models underlie particular procedures and what objective function is optimized to fit the model to the data, it enables readers to rapidly comprehend multivariate data analysis. Arranged so that readers can intuitively grasp the purposes for which multivariate analysis procedures are used, the book also offers clear explanations of those purposes, with numerical examples preceding the mathematical descriptions.

Supporting the modern matrix formulations by highlighting singular value decomposition among theorems in matrix algebra, this book is useful for undergraduate students who have already learned introductory statistics, as well as for graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis.

The book begins by explainingfundamental matrix operations and the matrix expressions of elementary statistics. Then, it offers an introduction to popular multivariate procedures, with each chapter featuring increasing advanced levels of matrix algebra.

Further the book includes in six chapters on advanced procedures, covering advanced matrix operations and recently proposed multivariate procedures, such as sparse estimation, together with a clear explication of the differences between principal components and factor analyses solutions. In a nutshell, this book allows readers to gain an understanding of the latest developments in multivariate data science.

Allows even readers with no knowledge of matrices to understand the operations for multivariate data analysis Highlights understanding which function is optimized to obtain a solution as the fastest way to capture a procedure Demonstrates multivariate procedures with numerical illustrations so that readers can intuitively grasp their usefulness

Autorentext
Kohei Adachi, Graduate School of Human Sciences, Osaka University

Inhalt

Elementary matrix operations.- Intravariable statistics.- Inter-variable statistics.- Regression analysis.- Principal component analysis.- Principal component.