Multivariate Data Analysis On Matrix Manifolds

Author : Nickolay Trendafilov,Michele Gallo
Publisher : Springer Nature
Page : 467 pages
File Size : 52,8 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9783030769741

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Multivariate Data Analysis on Matrix Manifolds by Nickolay Trendafilov,Michele Gallo Pdf

This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.

Author : Nickolay Trendafilov,Michele Gallo
Publisher : Unknown
Page : 0 pages
File Size : 52,7 Mb
Release : 2021
Category : Electronic
ISBN : 3030769755

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Multivariate Data Analysis on Matrix Manifolds by Nickolay Trendafilov,Michele Gallo Pdf

This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization. .

Author : Kohei Adachi
Publisher : Springer
Page : 298 pages
File Size : 46,6 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 : Nicolas Boumal
Publisher : Cambridge University Press
Page : 358 pages
File Size : 49,5 Mb
Release : 2023-03-16
Category : Mathematics
ISBN : 9781009178716

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An Introduction to Optimization on Smooth Manifolds by Nicolas Boumal Pdf

Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.

Author : Alan J. Izenman
Publisher : Springer Science & Business Media
Page : 757 pages
File Size : 49,8 Mb
Release : 2009-03-02
Category : Mathematics
ISBN : 9780387781891

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Modern Multivariate Statistical Techniques by Alan J. Izenman Pdf

This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.

Author : William W. Cooley,Paul R. Lohnes
Publisher : Unknown
Page : 392 pages
File Size : 40,8 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:49015001144485

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Multivariate Data Analysis by William W. Cooley,Paul R. Lohnes Pdf

Author : Paul E. Green,J. Douglas Carroll
Publisher : Unknown
Page : 546 pages
File Size : 45,8 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015036964016

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Analyzing Multivariate Data by Paul E. Green,J. Douglas Carroll Pdf

Single criterion, multiple predictor association; Multiple criterion, multiple predictor association; The analysis of interdependence.

Author : Anthony C. Atkinson,Marco Riani,Andrea Cerioli
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 47,9 Mb
Release : 2004-01-09
Category : Mathematics
ISBN : 0387408525

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Exploring Multivariate Data with the Forward Search by Anthony C. Atkinson,Marco Riani,Andrea Cerioli Pdf

S-PLUS programs for the forward search are available on a Web site." "This book is a companion to Atkinson and Riani's Robust Diagnostic Regression Analysis, of which the reviewer for The Journal of the Royal Statistical Society wrote, "I read this book, compulsive reading such as it was, in three sittings.""--Jacket.

Author : Piotr Mikusinski,Michael D. Taylor
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200734

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An Introduction to Multivariable Analysis from Vector to Manifold by Piotr Mikusinski,Michael D. Taylor Pdf

Multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This book takes the student and researcher on a journey through the core topics of the subject. Systematic exposition, with numerous examples and exercises from the computational to the theoretical, makes difficult ideas as concrete as possible. Good bibliography and index.

Author : Victor Patrangenaru,Leif Ellingson
Publisher : CRC Press
Page : 534 pages
File Size : 47,9 Mb
Release : 2015-09-18
Category : Mathematics
ISBN : 9781439820513

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Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis by Victor Patrangenaru,Leif Ellingson Pdf

A New Way of Analyzing Object Data from a Nonparametric ViewpointNonparametric Statistics on Manifolds and Their Applications to Object Data Analysis provides one of the first thorough treatments of the theory and methodology for analyzing data on manifolds. It also presents in-depth applications to practical problems arising in a variety of fields

Author : Marian Bubak,Geert D. van Albada,Peter M.A. Sloot,Jack Dongarra
Publisher : Springer Science & Business Media
Page : 1336 pages
File Size : 55,9 Mb
Release : 2004-05-25
Category : Computers
ISBN : 9783540221296

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Computational Science — ICCS 2004 by Marian Bubak,Geert D. van Albada,Peter M.A. Sloot,Jack Dongarra Pdf

The International Conference on Computational Science (ICCS 2004) held in Krak ́ ow, Poland, June 6–9, 2004, was a follow-up to the highly successful ICCS 2003 held at two locations, in Melbourne, Australia and St. Petersburg, Russia; ICCS 2002 in Amsterdam, The Netherlands; and ICCS 2001 in San Francisco, USA. As computational science is still evolving in its quest for subjects of inves- gation and e?cient methods, ICCS 2004 was devised as a forum for scientists from mathematics and computer science, as the basic computing disciplines and application areas, interested in advanced computational methods for physics, chemistry, life sciences, engineering, arts and humanities, as well as computer system vendors and software developers. The main objective of this conference was to discuss problems and solutions in all areas, to identify new issues, to shape future directions of research, and to help users apply various advanced computational techniques. The event harvested recent developments in com- tationalgridsandnextgenerationcomputingsystems,tools,advancednumerical methods, data-driven systems, and novel application ?elds, such as complex - stems, ?nance, econo-physics and population evolution.

Author : Kohei Adachi
Publisher : Unknown
Page : 301 pages
File Size : 41,9 Mb
Release : 2016
Category : Matrices
ISBN : 9811023425

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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 : Hair
Publisher : Pearson Education India
Page : 928 pages
File Size : 53,6 Mb
Release : 2007-09
Category : Analysis of variance
ISBN : 8131715280

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Multivariate Data Analysis by Hair Pdf

Author : Tõnu Kollo,D. von Rosen
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 47,9 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781402034190

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Advanced Multivariate Statistics with Matrices by Tõnu Kollo,D. von Rosen Pdf

The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.

Author : Chris Chatfield
Publisher : Routledge
Page : 197 pages
File Size : 44,5 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351436786

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Introduction to Multivariate Analysis by Chris Chatfield Pdf

This book provides an introduction to the analysis of multivariate data.It describes multivariate probability distributions, the preliminary analysisof a large -scale set of data, princ iple component and factor analysis,traditional normal theory material, as well as multidimensional scaling andcluster analysis.Introduction to Multivariate Analysis provides a reasonable blend oftheory and practice. Enough theory is given to introduce the concepts andto make the topics mathematically interesting. In addition the authors discussthe use (and misuse) of the techniques in pra ctice and present appropriatereal-life examples from a variety of areas includ ing agricultural research,soc iology and crim inology. The book should be suitable both for researchworkers and as a text for students taking a course on multivariate analysis.