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Author: Haruo Yanai
Publisher: Springer Science & Business Media
ISBN: 144199887X
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.
Author: Haruo Yanai
Publisher: Springer Science & Business Media
ISBN: 144199887X
Category : Mathematics
Languages : en
Pages : 244
Get Book Here
Book Description
Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.
Author: Marvin H. J. Gruber
Publisher: John Wiley & Sons
ISBN: 1118592557
Category : Mathematics
Languages : en
Pages : 391
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Book Description
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
Author: Kenichi Kanatani
Publisher: Springer Nature
ISBN: 303102544X
Category : Technology & Engineering
Languages : en
Pages : 141
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Book Description
Linear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstract high-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra.
Author: Yimin Wei
Publisher: World Scientific
ISBN: 9813238682
Category : Mathematics
Languages : en
Pages : 470
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Book Description
We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.
Author:
Publisher: Elsevier
ISBN: 0080448941
Category : Education
Languages : en
Pages : 6964
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Book Description
The field of education has experienced extraordinary technological, societal, and institutional change in recent years, making it one of the most fascinating yet complex fields of study in social science. Unequalled in its combination of authoritative scholarship and comprehensive coverage, International Encyclopedia of Education, Third Edition succeeds two highly successful previous editions (1985, 1994) in aiming to encapsulate research in this vibrant field for the twenty-first century reader. Under development for five years, this work encompasses over 1,000 articles across 24 individual areas of coverage, and is expected to become the dominant resource in the field. Education is a multidisciplinary and international field drawing on a wide range of social sciences and humanities disciplines, and this new edition comprehensively matches this diversity. The diverse background and multidisciplinary subject coverage of the Editorial Board ensure a balanced and objective academic framework, with 1,500 contributors representing over 100 countries, capturing a complete portrait of this evolving field. A totally new work, revamped with a wholly new editorial board, structure and brand-new list of meta-sections and articles Developed by an international panel of editors and authors drawn from senior academia Web-enhanced with supplementary multimedia audio and video files, hotlinked to relevant references and sources for further study Incorporates ca. 1,350 articles, with timely coverage of such topics as technology and learning, demography and social change, globalization, and adult learning, to name a few Offers two content delivery options - print and online - the latter of which provides anytime, anywhere access for multiple users and superior search functionality via ScienceDirect, as well as multimedia content, including audio and video files
Author: Herve Abdi
Publisher: Springer Science & Business Media
ISBN: 1461482836
Category : Mathematics
Languages : en
Pages : 351
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Book Description
New Perspectives in Partial Least Squares and Related Methods shares original, peer-reviewed research from presentations during the 2012 partial least squares methods meeting (PLS 2012). This was the 7th meeting in the series of PLS conferences and the first to take place in the USA. PLS is an abbreviation for Partial Least Squares and is also sometimes expanded as projection to latent structures. This is an approach for modeling relations between data matrices of different types of variables measured on the same set of objects. The twenty-two papers in this volume, which include three invited contributions from our keynote speakers, provide a comprehensive overview of the current state of the most advanced research related to PLS and related methods. Prominent scientists from around the world took part in PLS 2012 and their contributions covered the multiple dimensions of the partial least squares-based methods. These exciting theoretical developments ranged from partial least squares regression and correlation, component based path modeling to regularized regression and subspace visualization. In following the tradition of the six previous PLS meetings, these contributions also included a large variety of PLS approaches such as PLS metamodels, variable selection, sparse PLS regression, distance based PLS, significance vs. reliability, and non-linear PLS. Finally, these contributions applied PLS methods to data originating from the traditional econometric/economic data to genomics data, brain images, information systems, epidemiology, and chemical spectroscopy. Such a broad and comprehensive volume will also encourage new uses of PLS models in work by researchers and students in many fields.
Author: Dennis S. Bernstein
Publisher: Princeton University Press
ISBN: 0691176531
Category : Mathematics
Languages : en
Pages : 1593
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Book Description
The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index
Author: Tamara Radivilova
Publisher: Springer Nature
ISBN: 3030430707
Category : Technology & Engineering
Languages : en
Pages : 789
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Book Description
This book addresses the challenges and opportunities of information/data processing and management. It also covers a range of methods, techniques and strategies for making it more efficient, approaches to increasing its usage, and ways to minimize information/data loss while improving customer satisfaction. Information and Communication Technologies (ICTs) and the Service Systems associated with them have had an enormous impact on businesses and our day-to-day lives over the past three decades, and continue to do so. This development has led to the emergence of new application areas and relevant disciplines, which in turn present new challenges and opportunities for service system usage. The book provides practical insights into various aspects of ICT technologies for service systems: Techniques for information/data processing and modeling in service systems Strategies for the provision of information/data processing and management Methods for collecting and analyzing information/data Applications, benefits, and challenges of service system implementation Solutions to increase the performance of various service systems using the latest ICT technologies
Author: Kohei Adachi
Publisher: Springer
ISBN: 9811023417
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
Author: Giuseppe De Pietro
Publisher: Springer
ISBN: 3319393456
Category : Technology & Engineering
Languages : en
Pages : 725
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Book Description
This book contains the contributions presented at the ninth international KES conference on Intelligent Interactive Multimedia: Systems and Services, which took place in Puerto de la Cruz, Tenerife, Spain, June 15-17, 2016. It contains 65 peer-reviewed book chapters that focus on issues ranging from intelligent image or video storage, retrieval, transmission and analysis to knowledge-based technologies, from advanced information technology architectures for video processing and transmission to advanced functionalities of information and knowledge-based services. We believe that this book will serve as a useful source of knowledge for both academia and industry, for all those faculty members, research scientists, scholars, Ph.D. students and practitioners, who are interested in fundamental and applied facets of intelligent interactive multimedia.
