Multivariate Data Analysis On Matrix Manifolds PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Multivariate Data Analysis On Matrix Manifolds PDF full book. Access full book title Multivariate Data Analysis On Matrix Manifolds.
Author | : Nickolay Trendafilov |
Publisher | : Springer Nature |
Total Pages | : 467 |
Release | : 2021-09-15 |
Genre | : Mathematics |
ISBN | : 3030769747 |
Download Multivariate Data Analysis on Matrix Manifolds Book in PDF, ePub and Kindle
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 |
Publisher | : |
Total Pages | : 0 |
Release | : 2021 |
Genre | : |
ISBN | : 9783030769758 |
Download Multivariate Data Analysis on Matrix Manifolds Book in PDF, ePub and Kindle
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 Nature |
Total Pages | : 457 |
Release | : 2020-05-20 |
Genre | : Mathematics |
ISBN | : 9811541035 |
Download Matrix-Based Introduction to Multivariate Data Analysis Book in PDF, ePub and Kindle
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.
Author | : Kohei Adachi |
Publisher | : Springer |
Total Pages | : 298 |
Release | : 2016-10-11 |
Genre | : Mathematics |
ISBN | : 9811023417 |
Download Matrix-Based Introduction to Multivariate Data Analysis Book in PDF, ePub and Kindle
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 |
Total Pages | : 358 |
Release | : 2023-03-16 |
Genre | : Mathematics |
ISBN | : 1009178717 |
Download An Introduction to Optimization on Smooth Manifolds Book in PDF, ePub and Kindle
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 | : William W. Cooley |
Publisher | : |
Total Pages | : 392 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : |
Download Multivariate Data Analysis Book in PDF, ePub and Kindle
Author | : Kim H. Esbensen |
Publisher | : Multivariate Data Analysis |
Total Pages | : 622 |
Release | : 2002 |
Genre | : Experimental design |
ISBN | : 9788299333030 |
Download Multivariate Data Analysis Book in PDF, ePub and Kindle
"Multivariate Data Analysis - in practice adopts a practical, non-mathematical approach to multivariate data analysis. The book's principal objective is to provide a conceptual framework for multivariate data analysis techniques, enabling the reader to apply these in his or her own field. Features: Focuses on the practical application of multivariate techniques such as PCA, PCR and PLS and experimental design. Non-mathematical approach - ideal for analysts with little or no background in statistics. Step by step introduction of new concepts and techniques promotes ease of learning. Theory supported by hands-on exercises based on real-world data. A full training copy of The Unscrambler (for Windows 95, Windows NT 3.51 or later versions) including data sets for the exercises is available. Tutorial exercises based on data from real-world applications are used throughout the book to illustrate the use of the techniques introduced, providing the reader with a working knowledge of modern multivariate data analysis and experimental design. All exercises use The Unscrambler, a de facto industry standard for multivariate data analysis software packages. Multivariate Data Analysis in Practice is an excellent self-study text for scientists, chemists and engineers from all disciplines (non-statisticians) wishing to exploit the power of practical multivariate methods. It is very suitable for teaching purposes at the introductory level, and it can always be supplemented with higher level theoretical literature."Résumé de l'éditeur.
Author | : Victor Patrangenaru |
Publisher | : CRC Press |
Total Pages | : 534 |
Release | : 2015-09-18 |
Genre | : Mathematics |
ISBN | : 1439820511 |
Download Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis Book in PDF, ePub and Kindle
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 | : Piotr Mikusinski |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461200733 |
Download An Introduction to Multivariable Analysis from Vector to Manifold Book in PDF, ePub and Kindle
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 | : Barbara Bund |
Publisher | : McGraw-Hill/Irwin |
Total Pages | : 268 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : |
Download Multivariate Data Analysis Book in PDF, ePub and Kindle