Multivariate Data Analysis on Matrix Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multivariate Data Analysis on Matrix Manifolds write by Nickolay Trendafilov. This book was released on 2021-09-15. Multivariate Data Analysis on Matrix Manifolds available 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.
Multivariate Data Analysis on Matrix Manifolds
Multivariate Data Analysis on Matrix Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multivariate Data Analysis on Matrix Manifolds write by Nickolay Trendafilov. This book was released on 2021. Multivariate Data Analysis on Matrix Manifolds available 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. .
Matrix-Based Introduction to Multivariate Data Analysis
Matrix-Based Introduction to Multivariate Data Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Matrix-Based Introduction to Multivariate Data Analysis write by Kohei Adachi. This book was released on 2016-10-11. Matrix-Based Introduction to Multivariate Data Analysis available 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.
An Introduction to Optimization on Smooth Manifolds
An Introduction to Optimization on Smooth Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Optimization on Smooth Manifolds write by Nicolas Boumal. This book was released on 2023-03-16. An Introduction to Optimization on Smooth Manifolds available 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.
Multivariate Data Analysis
Multivariate Data Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multivariate Data Analysis write by William W. Cooley. This book was released on 1985. Multivariate Data Analysis available in PDF, EPUB and Kindle.
