Matrix-Based Introduction to Multivariate Data Analysis

Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-981-10-9595-5
Verlag: Springer Nature Singapore

Buch, Englisch, 301 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 482 g

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

Zielgruppe

Graduate

Autoren/Hrsg.

Adachi, Kohei

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Part 1. Elementary Statistics with Matrices.- 1 Introduction to Matrix Operations.- 2 Intra-variable Statistics.- 3 Inter-variable Statistics.- Part 2. Least Squares Procedures.- 4 Regression Analysis.- 5 Principal Component Analysis (Part 1).- 6 Principal Component Analysis 2 (Part 2).- 7 Cluster Analysis.- Part 3. Maximum Likelihood Procedures.- 8 Maximum Likelihood and Normal Distributions.- 9 Path Analysis.- 10 Confirmatory Factor Analysis.- 11 Structural Equation Modeling.- 12 Exploratory Factor Analysis.- Part 4. Miscellaneous Procedures.- 13 Rotation Techniques.- 14 Canonical Correlation and Multiple Correspondence Analyses.- 15 Discriminant Analysis.- 16 Multidimensional Scaling.- Appendices.- A1 Geometric Understanding of Matrices and Vectors.-  A2 Decomposition of Sums of Squares.-  A3 Singular Value Decomposition (SVD).- A4 Matrix Computation Using SVD.- A5 Supplements for Probability Densities and Likelihoods.- A6 Iterative Algorithms.- References.- Index.

Über Autor(innen)

Kohei Adachi, Graduate School of Human Sciences, Osaka University