國立虎尾科技大學 |

Matrix-based introduction to multivariate data analysis

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Matrix-based introduction to multivariate data analysis/ by Kohei Adachi.
Author:	Adachi, Kohei.
Published:	Singapore :Springer Singapore : : 2016.,
Description:	xi, 301 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Multivariate analysis. -
Online resource:	http://dx.doi.org/10.1007/978-981-10-2341-5
ISBN:	9789811023415

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

Matrix-based introduction to multivariate data analysis[electronic resource] /by Kohei Adachi. - Singapore :Springer Singapore :2016. - xi, 301 p. :ill. (some col.), digital ;24 cm.

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.

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.

ISBN: 9789811023415

Standard No.: 10.1007/978-981-10-2341-5doiSubjects--Topical Terms:

577402
Multivariate analysis.

LC Class. No.: QA278

Dewey Class. No.: 519.535

Matrix-based introduction to multivariate data analysis
LDR:03423nam a2200313 a 4500 001 867806
003 DE-He213
005 20161011130355.0
006 m d
007 cr nn 008maaau
008 170720s2016 si s 0 eng d
020 $a 9789811023415 $q (electronic bk.)
020 $a 9789811023408 $q (paper)
024 7 $a 10.1007/978-981-10-2341-5 $2 doi
035 $a 978-981-10-2341-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA278
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
082 0 4 $a 519.535 $2 23
090 $a QA278 $b .A191 2016
100 1 $a Adachi, Kohei. $3 1114915
245 1 0 $a Matrix-based introduction to multivariate data analysis $h [electronic resource] / $c by Kohei Adachi.
260 $a Singapore : $c 2016. $b Springer Singapore : $b Imprint: Springer,
300 $a xi, 301 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Multivariate analysis. $3 577402
650 0 $a Matrices. $3 528174
650 1 4 $a Statistics. $3 556824
650 2 4 $a Statistical Theory and Methods. $3 671396
650 2 4 $a Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. $3 782247
650 2 4 $a Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. $3 670129
650 2 4 $a Statistics and Computing/Statistics Programs. $3 669775
650 2 4 $a Statistics for Business/Economics/Mathematical Finance/Insurance. $3 669275
650 2 4 $a Probability and Statistics in Computer Science. $3 669886
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-2341-5
950 $a Mathematics and Statistics (Springer-11649)