Multivariate Data Analysis On Matrix Manifolds
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Multivariate Data Analysis On Matrix Manifolds
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Author : Nickolay Trendafilov
language : en
Publisher: Springer Nature
Release Date : 2021-09-15
Multivariate Data Analysis On Matrix Manifolds written by Nickolay Trendafilov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-15 with Mathematics categories.
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
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Author : Kohei Adachi
language : en
Publisher: Springer Nature
Release Date : 2020-05-20
Matrix Based Introduction To Multivariate Data Analysis written by Kohei Adachi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-20 with Mathematics categories.
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.
An Introduction To Optimization On Smooth Manifolds
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Author : Nicolas Boumal
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-16
An Introduction To Optimization On Smooth Manifolds written by Nicolas Boumal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-16 with Mathematics categories.
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.
Methodological And Applied Statistics And Demography Ii
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Author : Alessio Pollice
language : en
Publisher: Springer Nature
Release Date : 2025-03-02
Methodological And Applied Statistics And Demography Ii written by Alessio Pollice and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-02 with Mathematics categories.
This book of peer-reviewed short papers on methodological and applied statistics and demography is the second of four volumes from the 52nd Scientific Meeting of the Italian Statistical Society (SIS 2024), held in Bari, Italy, on June 17-20, 2024. It features invited contributions presented in the Solicited Sessions. The volumes address a large number of topics and applications of current interest. The topics covered include, but are not limited to, statistical theory and methods, sampling theory, Bayesian statistics, statistical modeling, computational statistics, classification, data analysis, gender statistics and applied statistics. The applications reflect new analyses in a wide variety of fields, including demography, psychometrics, education, business, economics, finance, law, and other social sciences and humanities, epidemiology, the life and health sciences as well as the environmental and natural sciences and engineering. This variety also demonstrates the important role of statistical science in addressing the societal and environmental challenges of sustainable development. One of the aims of the Italian Statistical Society (SIS) is to promote scientific activities for the development of statistical sciences. Its biennial international Scientific Meeting represents the Society’s largest event which brings together national and international researchers and professionals to exchange ideas and discuss recent advances and developments in theoretical and applied statistics.
Advanced Methods In Statistics Data Science And Related Applications
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Author : Matilde Bini
language : en
Publisher: Springer Nature
Release Date : 2024-10-16
Advanced Methods In Statistics Data Science And Related Applications written by Matilde Bini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-16 with Computers categories.
This book contains a selection of the improved contributions submitted by participants at the conference of the Italian Statistical Society - SIS 2022 held in Caserta 22-24 June 2022. The scientific community of Italian statistics, which gathers around the SIS, is paying particular attention to the development of statistical techniques increasingly oriented toward the processing of large data, mainly, of complex data. The main goal is to provide the analysis of the data and the interpretability of the obtained results, with a view to decision support and the reliability of the data outcomes. The aim of this volume is to show some of the most relevant contributions of statistical and data analysis methods in preserving the quality of the information to be processed, especially when it comes from different, often non-official sources; as well as in the extraction of knowledge from complex data (textual, network, unstructured and multivalue) and in the explicability of results. Data Science today represents a broad domain of knowledge development from data, where statistical and data analysis methods can make an important contribution in the different domains where data management and processing are required. This volume is addressed to researchers but also to Ph.D. and MSc students in the field of Statistics and Data Science to acquaint them with some of the most recent developments towards which statistical research is orienting, in prevalence in Italy.
Nonparametric Statistics On Manifolds And Their Applications To Object Data Analysis
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Author : Victor Patrangenaru
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Nonparametric Statistics On Manifolds And Their Applications To Object Data Analysis written by Victor Patrangenaru and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
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
Massive Mimo For Future Wireless Communication Systems
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Author : Webert Montlouis
language : en
Publisher: John Wiley & Sons
Release Date : 2025-01-15
Massive Mimo For Future Wireless Communication Systems written by Webert Montlouis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-15 with Computers categories.
Authoritative resource discussing the development of advanced massive multiple input multiple output (MIMO) techniques and algorithms for application in 6G Massive MIMO for Future Wireless Communication Systems analyzes applications and technology trends for massive multiple input multiple output (MIMO) in 6G and beyond, presenting a unified theoretical framework for analyzing the fundamental limits of massive MIMO that considers several practical constraints. In addition, this book develops advanced signal-processing algorithms to enable massive MIMO applications in realistic environments. The book looks closer at applying techniques to massive MIMO in order to meet practical network constraints in 6G networks, such as interference, pathloss, delay, and traffic outage, and provides new insights into real-world deployment scenarios, applications, management, and associated benefits of robust, provably secure, and efficient security and privacy schemes for massive MIMO wireless communication networks. To aid in reader comprehension, this book includes a glossary of terms, resources for further reading via a detailed bibliography, and useful figures and summary tables throughout. With contributions from industry experts and researchers across the world and edited by two leaders in the field, Massive MIMO for Future Wireless Communication Systems includes information on: Signal processing algorithms for cell-free massive MIMO systems and advanced mathematical tools to analyze multiuser dynamics in wireless channels Bit error rate (BER) performance comparisons of different detectors in conventional cell-free massive MIMO systems Enhancement of massive MIMO using deep learning-based channel estimation and cell-free massive MIMO for wireless federated learning Low-complexity, self-organizing, and energy-efficient massive MIMO architectures, including the prospects and challenges of Terahertz MIMO systems Massive MIMO for Future Wireless Communication Systems is an essential resource on the subject for industry and academic researchers, advanced students, scientists, and engineers in the fields of MIMO, antennas, sensing and channel measurements, and modeling technologies.
Statistics On Special Manifolds
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Author : Yasuko Chikuse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-12
Statistics On Special Manifolds written by Yasuko Chikuse and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-12 with Mathematics categories.
The special manifolds of interest in this book are the Stiefel manifold and the Grassmann manifold. Formally, the Stiefel manifold Vk,m is the space of k frames in the m-dimensional real Euclidean space Rm, represented by the set of m x k matrices X such that X' X = I , where Ik is the k x k identity matrix, k and the Grassmann manifold Gk,m-k is the space of k-planes (k-dimensional hyperplanes) in Rm. We see that the manifold Pk,m-k of m x m orthogonal projection matrices idempotent of rank k corresponds uniquely to Gk,m-k. This book is concerned with statistical analysis on the manifolds Vk,m and Pk,m-k as statistical sample spaces consisting of matrices. The discussion is carried out on the real spaces so that scalars, vectors, and matrices treated in this book are all real, unless explicitly stated otherwise. For the special case k = 1, the observations from V1,m and G1,m-l are regarded as directed vectors on a unit sphere and as undirected axes or lines, respectively. There exists a large literature of applications of directional statis tics and its statistical analysis, mostly occurring for m = 2 or 3 in practice, in the Earth (or Geological) Sciences, Astrophysics, Medicine, Biology, Meteo rology, Animal Behavior, and many other fields. Examples of observations on the general Grassmann manifold Gk,m-k arise in the signal processing of radar with m elements observing k targets.
Computational Science Iccs 2004
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Author : Marian Bubak
language : en
Publisher: Springer
Release Date : 2004-10-11
Computational Science Iccs 2004 written by Marian Bubak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Computers categories.
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.
Directional Statistics
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Author : Kanti V. Mardia
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Directional Statistics written by Kanti V. Mardia and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.
Presents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work. The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent material on correlation, regression time series, robust techniques, bootstrap methods, density estimation and curve fitting is presented. The third part considers statistics on more general sample spaces, in particular rotation groups, Stiefel manifolds, Grassmann manifolds and complex projective spaces. Shape analysis is considered from the perspective of directional statistics. Written by leading authors in the field, this text will be invaluable not only to researchers in probability and statistics interested in the latest developments in directional statistics, but also to practitioners and researchers in many scientific fields, including astronomy, biology, computer vision, earth sciences and image analysis.