Multivariate Data Analysis On Matrix Manifolds PDF Download
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| 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 |
| 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 | : Paul E. Green |
| Publisher | : |
| Total Pages | : 546 |
| Release | : 1978 |
| Genre | : Mathematics |
| ISBN | : |
Download Analyzing Multivariate Data Book in PDF, ePub and Kindle
Single criterion, multiple predictor association; Multiple criterion, multiple predictor association; The analysis of interdependence.
| Author | : Kohei Adachi |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2020 |
| Genre | : Electronic books |
| ISBN | : 9789811541049 |
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 | : 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 | : Alan J. Izenman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 757 |
| Release | : 2009-03-02 |
| Genre | : Mathematics |
| ISBN | : 0387781897 |
Download Modern Multivariate Statistical Techniques Book in PDF, ePub and Kindle
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 | : P.-A. Absil |
| Publisher | : Princeton University Press |
| Total Pages | : 240 |
| Release | : 2009-04-11 |
| Genre | : Mathematics |
| ISBN | : 9781400830244 |
Download Optimization Algorithms on Matrix Manifolds Book in PDF, ePub and Kindle
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
