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Matrix-based introduction to multivariate data analysis / Kohei Adachi.

Adachi, Kohei, author.
2016
QA278
Available Online
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Title
Matrix-based introduction to multivariate data analysis / Kohei Adachi.
Author
Adachi, Kohei, author.
ISBN
9789811023415 (electronic book)
9811023417 (electronic book)
9789811023408
DOI
https://doi.org/10.1007/978-981-10-2341-5
Published
Singapore : Springer, 2016.
Language
English
Description
1 online resource (xi, 301 pages) : illustrations.
Item Number
10.1007/978-981-10-2341-5 doi
Call Number
QA278
Dewey Decimal Classification
519.5/35
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed October 20, 2016).
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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.

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