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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 explaining fundamental 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.
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 explaining fundamental 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.
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.
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