Geometric Data Analysis
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Geometric Data Analysis
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Author : Brigitte Le Roux
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
Geometric Data Analysis written by Brigitte Le Roux 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 2006-01-16 with Mathematics categories.
Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself; it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.
Mathematical Principles Of Topological And Geometric Data Analysis
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Author : Parvaneh Joharinad
language : en
Publisher: Springer Nature
Release Date : 2023-07-29
Mathematical Principles Of Topological And Geometric Data Analysis written by Parvaneh Joharinad and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately. Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
Riemannian Geometric Statistics In Medical Image Analysis
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Author : Xavier Pennec
language : en
Publisher: Academic Press
Release Date : 2019-09-04
Riemannian Geometric Statistics In Medical Image Analysis written by Xavier Pennec and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-04 with Computers categories.
Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science.
Combinatorial Inference In Geometric Data Analysis
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Author : Brigitte Le Roux
language : en
Publisher: CRC Press
Release Date : 2019-03-20
Combinatorial Inference In Geometric Data Analysis written by Brigitte Le Roux and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.
Geometric Data Analysis designates the approach of Multivariate Statistics that conceptualizes the set of observations as a Euclidean cloud of points. Combinatorial Inference in Geometric Data Analysis gives an overview of multidimensional statistical inference methods applicable to clouds of points that make no assumption on the process of generating data or distributions, and that are not based on random modelling but on permutation procedures recasting in a combinatorial framework. It focuses particularly on the comparison of a group of observations to a reference population (combinatorial test) or to a reference value of a location parameter (geometric test), and on problems of homogeneity, that is the comparison of several groups for two basic designs. These methods involve the use of combinatorial procedures to build a reference set in which we place the data. The chosen test statistics lead to original extensions, such as the geometric interpretation of the observed level, and the construction of a compatibility region. Features: Defines precisely the object under study in the context of multidimensional procedures, that is clouds of points Presents combinatorial tests and related computations with R and Coheris SPAD software Includes four original case studies to illustrate application of the tests Includes necessary mathematical background to ensure it is self–contained This book is suitable for researchers and students of multivariate statistics, as well as applied researchers of various scientific disciplines. It could be used for a specialized course taught at either master or PhD level.
Geometric Data Analysis
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Author : Michael Kirby
language : de
Publisher: Wiley-Interscience
Release Date : 2001-01-12
Geometric Data Analysis written by Michael Kirby and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-12 with Computers categories.
This book addresses the most efficient methods of pattern analysis using wavelet decomposition. Readers will learn to analyze data in order to emphasize the differences between closely related patterns and then categorize them in a way that is useful to system users.
Topological Data Analysis With Applications
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Author : Gunnar Carlsson
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Topological Data Analysis With Applications written by Gunnar Carlsson 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 2021-12-16 with Computers categories.
This timely text introduces topological data analysis from scratch, with detailed case studies.
Functional And Shape Data Analysis
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Author : Anuj Srivastava
language : en
Publisher: Springer
Release Date : 2016-10-03
Functional And Shape Data Analysis written by Anuj Srivastava and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-03 with Mathematics categories.
This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.
Geometric Analysis
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Author : Ailana Fraser
language : en
Publisher: Springer Nature
Release Date : 2020-08-20
Geometric Analysis written by Ailana Fraser and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-20 with Mathematics categories.
This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces. An output of the CIME Summer School "Geometric Analysis" held in Cetraro in 2018, it offers a collection of lecture notes prepared by Ailana Fraser (UBC), André Neves (Chicago), Peter M. Topping (Warwick), and Paul C. Yang (Princeton). These notes will be a valuable asset for researchers and advanced graduate students in geometric analysis.
Computational Topology For Data Analysis
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Author : Tamal Krishna Dey
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-10
Computational Topology For Data Analysis written by Tamal Krishna Dey 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 2022-03-10 with Computers categories.
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Image Processing And Data Analysis
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Author : Jean-Luc Starck
language : en
Publisher: Cambridge University Press
Release Date : 1998
Image Processing And Data Analysis written by Jean-Luc Starck 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 1998 with Image processing categories.
Powerful techniques have been developed in recent years for the analysis of digital data, especially the manipulation of images. This book provides an in-depth introduction to a range of these innovative, avante-garde data-processing techniques. It develops the reader's understanding of each technique and then shows with practical examples how they can be applied to improve the skills of graduate students and researchers in astronomy, electrical engineering, physics, geophysics and medical imaging. What sets this book apart from others on the subject is the complementary blend of theory and practical application. Throughout, it is copiously illustrated with real-world examples from astronomy, electrical engineering, remote sensing and medicine. It also shows how many, more traditional, methods can be enhanced by incorporating the new wavelet and multiscale methods into the processing. For graduate students and researchers already experienced in image processing and data analysis, this book provides an indispensable guide to a wide range of exciting and original data-analysis techniques.