Projection Matrices Generalized Inverse Matrices And Singular Value Decomposition

Author : Haruo Yanai,Kei Takeuchi,Yoshio Takane
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 41,5 Mb
Release : 2011-04-06
Category : Mathematics
ISBN : 9781441998873

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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition by Haruo Yanai,Kei Takeuchi,Yoshio Takane Pdf

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
Page : 391 pages
File Size : 48,7 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9781118592557

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Matrix Algebra for Linear Models by Marvin H. J. Gruber Pdf

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
Page : 141 pages
File Size : 42,6 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031025440

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Linear Algebra for Pattern Processing by Kenichi Kanatani Pdf

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 : Anonim
Publisher : Elsevier
Page : 6964 pages
File Size : 55,7 Mb
Release : 2009-04-17
Category : Education
ISBN : 9780080448947

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International Encyclopedia of Education by Anonim Pdf

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 : Guorong Wang,Yimin Wei,Sanzheng Qiao
Publisher : Springer
Page : 378 pages
File Size : 53,6 Mb
Release : 2018-05-12
Category : Mathematics
ISBN : 9789811301469

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Generalized Inverses: Theory and Computations by Guorong Wang,Yimin Wei,Sanzheng Qiao Pdf

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

Author : Herve Abdi,Wynne W. Chin,Vincenzo Esposito Vinzi,Giorgio Russolillo,Laura Trinchera
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 46,7 Mb
Release : 2013-10-17
Category : Mathematics
ISBN : 9781461482833

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New Perspectives in Partial Least Squares and Related Methods by Herve Abdi,Wynne W. Chin,Vincenzo Esposito Vinzi,Giorgio Russolillo,Laura Trinchera Pdf

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
Page : 1593 pages
File Size : 46,6 Mb
Release : 2018-02-27
Category : Mathematics
ISBN : 9780691176536

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Scalar, Vector, and Matrix Mathematics by Dennis S. Bernstein Pdf

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 : Kohei Adachi
Publisher : Springer
Page : 298 pages
File Size : 42,9 Mb
Release : 2016-10-11
Category : Mathematics
ISBN : 9789811023415

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Matrix-Based Introduction to Multivariate Data Analysis by Kohei Adachi Pdf

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 : Thomas W. Yee
Publisher : Springer
Page : 589 pages
File Size : 43,7 Mb
Release : 2015-09-11
Category : Mathematics
ISBN : 9781493928187

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Vector Generalized Linear and Additive Models by Thomas W. Yee Pdf

This book presents a greatly enlarged statistical framework compared to generalized linear models (GLMs) with which to approach regression modelling. Comprising of about half-a-dozen major classes of statistical models, and fortified with necessary infrastructure to make the models more fully operable, the framework allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. However, GLMs are not flexible enough to cope with the demands of practical data analysis. And data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. The methodology here and accompanying software (the extensive VGAM R package) are directed at these limitations and are described comprehensively for the first time in one volume. This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs. The book can be used in senior undergraduate or first-year postgraduate courses on GLMs or categorical data analysis and as a methodology resource for VGAM users. In the second part of the book, the R package VGAM allows readers to grasp immediately applications of the methodology. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences. The methodological contribution of this book stands alone and does not require use of the VGAM package.

Author : Tamara Radivilova,Dmytro Ageyev,Natalia Kryvinska
Publisher : Springer Nature
Page : 789 pages
File Size : 40,7 Mb
Release : 2020-06-20
Category : Technology & Engineering
ISBN : 9783030430702

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Data-Centric Business and Applications by Tamara Radivilova,Dmytro Ageyev,Natalia Kryvinska Pdf

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 : Giuseppe De Pietro,Luigi Gallo,Robert J. Howlett,Lakhmi C. Jain
Publisher : Springer
Page : 741 pages
File Size : 44,5 Mb
Release : 2016-06-03
Category : Technology & Engineering
ISBN : 9783319393452

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Intelligent Interactive Multimedia Systems and Services 2016 by Giuseppe De Pietro,Luigi Gallo,Robert J. Howlett,Lakhmi C. Jain Pdf

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.

Author : Gustavo Carvajal,Marko Maucec,Stan Cullick
Publisher : Gulf Professional Publishing
Page : 374 pages
File Size : 48,7 Mb
Release : 2017-12-14
Category : Technology & Engineering
ISBN : 9780128047477

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Intelligent Digital Oil and Gas Fields by Gustavo Carvajal,Marko Maucec,Stan Cullick Pdf

Intelligent Digital Oil and Gas Fields: Concepts, Collaboration, and Right-time Decisions delivers to the reader a roadmap through the fast-paced changes in the digital oil field landscape of technology in the form of new sensors, well mechanics such as downhole valves, data analytics and models for dealing with a barrage of data, and changes in the way professionals collaborate on decisions. The book introduces the new age of digital oil and gas technology and process components and provides a backdrop to the value and experience industry has achieved from these in the last few years. The book then takes the reader on a journey first at a well level through instrumentation and measurement for real-time data acquisition, and then provides practical information on analytics on the real-time data. Artificial intelligence techniques provide insights from the data. The road then travels to the "integrated asset" by detailing how companies utilize Integrated Asset Models to manage assets (reservoirs) within DOF context. From model to practice, new ways to operate smart wells enable optimizing the asset. Intelligent Digital Oil and Gas Fields is packed with examples and lessons learned from various case studies and provides extensive references for further reading and a final chapter on the "next generation digital oil field," e.g., cloud computing, big data analytics and advances in nanotechnology. This book is a reference that can help managers, engineers, operations, and IT experts understand specifics on how to filter data to create useful information, address analytics, and link workflows across the production value chain enabling teams to make better decisions with a higher degree of certainty and reduced risk. Covers multiple examples and lessons learned from a variety of reservoirs from around the world and production situations Includes techniques on change management and collaboration Delivers real and readily applicable knowledge on technical equipment, workflows and data challenges such as acquisition and quality control that make up the digital oil and gas field solutions of today Describes collaborative systems and ways of working and how companies are transitioning work force to use the technology and making more optimal decisions

Author : Zeyu Wang,Weijian Liu,Hongmeng Chen
Publisher : CRC Press
Page : 195 pages
File Size : 48,5 Mb
Release : 2024-06-14
Category : Technology & Engineering
ISBN : 9781040030424

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Adaptive Detection for Multichannel Signals in Non-Ideal Environments by Zeyu Wang,Weijian Liu,Hongmeng Chen Pdf

This book systematically presents adaptive multichannel signal detection in three types of non-ideal environments, including sample-starved scenarios, signal mismatch scenarios, and noise plus subspace interference environments. The authors provide definitions of key concepts, detailed derivations of adaptive multichannel signal detectors, and specific examples for each non-ideal environment. In addition, the possible future trend of adaptive detection methods is discussed, as well as two further research points – namely, the adaptive detection algorithms based on information geometry, and the hybrid approaches that combine adaptive detection algorithms with machine learning algorithms. The book will be of interest to researchers, advanced undergraduates, and graduate students in sonar, radar signal processing, and communications engineering.

Author : Mutamed Khatib
Publisher : BoD – Books on Demand
Page : 256 pages
File Size : 51,8 Mb
Release : 2014-11-26
Category : Technology & Engineering
ISBN : 9789535117322

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Contemporary Issues in Wireless Communications by Mutamed Khatib Pdf

Wireless communications have a strong impact on improving the quality of life in this century. Smart phones industry is now considered one of the most attractive fields, so advanced research is conducted in order to improve the quality of service in wireless communication environments. Many design challenges such as power consumption, quality of service, low cost, high data rate and small size are being treated every day. This book aims to provide highlights of the current research in the field of wireless communications. The subjects discussed are very valuable to communication researchers as well as researchers in the wireless related areas. The book chapters cover a wide range of wireless communication topics that are considered key technologies for future applications.

Author : James E. Gentle
Publisher : Springer Nature
Page : 714 pages
File Size : 54,8 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031421440

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Matrix Algebra by James E. Gentle Pdf