Geometric Data Analysis

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Geometric Data Analysis

Brigitte Le Roux,Henry Rouanet
Geometric Data Analysis Book PDF

Author : Brigitte Le Roux,Henry Rouanet
Publisher : Springer Science & Business Media
Page : 475 pages
File Size : 45,5 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9781402022364

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Geometric Data Analysis by Brigitte Le Roux,Henry Rouanet Pdf

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.

Combinatorial Inference in Geometric Data Analysis

Brigitte Le Roux,Solène Bienaise,Jean-Luc Durand
Combinatorial Inference in Geometric Data Analysis Book PDF

Author : Brigitte Le Roux,Solène Bienaise,Jean-Luc Durand
Publisher : CRC Press
Page : 256 pages
File Size : 52,5 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9781498781626

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Combinatorial Inference in Geometric Data Analysis by Brigitte Le Roux,Solène Bienaise,Jean-Luc Durand Pdf

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

Michael Kirby
Geometric Data Analysis Book PDF

Author : Michael Kirby
Publisher : Wiley-Interscience
Page : 0 pages
File Size : 51,9 Mb
Release : 2001-01-12
Category : Computers
ISBN : 0471239291

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Geometric Data Analysis by Michael Kirby Pdf

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.

Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Jianzhong Wang
Geometric Structure of High Dimensional Data and Dimensionality Reduction Book PDF

Author : Jianzhong Wang
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 52,8 Mb
Release : 2012-04-28
Category : Computers
ISBN : 9783642274978

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Geometric Structure of High-Dimensional Data and Dimensionality Reduction by Jianzhong Wang Pdf

"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.

Mathematical Principles of Topological and Geometric Data Analysis

Parvaneh Joharinad,Jürgen Jost
Mathematical Principles of Topological and Geometric Data Analysis Book PDF

Author : Parvaneh Joharinad,Jürgen Jost
Publisher : Unknown
Page : 0 pages
File Size : 53,6 Mb
Release : 2023
Category : Electronic
ISBN : 3031334418

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Mathematical Principles of Topological and Geometric Data Analysis by Parvaneh Joharinad,Jürgen Jost Pdf

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

Xavier Pennec,Stefan Sommer,Tom Fletcher
Riemannian Geometric Statistics in Medical Image Analysis Book PDF

Author : Xavier Pennec,Stefan Sommer,Tom Fletcher
Publisher : Academic Press
Page : 636 pages
File Size : 46,7 Mb
Release : 2019-09-02
Category : Computers
ISBN : 9780128147269

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Riemannian Geometric Statistics in Medical Image Analysis by Xavier Pennec,Stefan Sommer,Tom Fletcher Pdf

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. A complete reference covering both the foundations and state-of-the-art methods Edited and authored by leading researchers in the field Contains theory, examples, applications, and algorithms Gives an overview of current research challenges and future applications

Mathematical Principles of Topological and Geometric Data Analysis

Parvaneh Joharinad,Jürgen Jost
Mathematical Principles of Topological and Geometric Data Analysis Book PDF

Author : Parvaneh Joharinad,Jürgen Jost
Publisher : Springer Nature
Page : 287 pages
File Size : 43,8 Mb
Release : 2023-07-29
Category : Mathematics
ISBN : 9783031334405

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Mathematical Principles of Topological and Geometric Data Analysis by Parvaneh Joharinad,Jürgen Jost Pdf

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.

Computational Topology for Data Analysis

Tamal Krishna Dey,Yusu Wang
Computational Topology for Data Analysis Book PDF

Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 45,6 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Geometric Analysis

Ailana Fraser,André Neves,Peter M. Topping,Paul C. Yang
Geometric Analysis Book PDF

Author : Ailana Fraser,André Neves,Peter M. Topping,Paul C. Yang
Publisher : Springer Nature
Page : 146 pages
File Size : 50,9 Mb
Release : 2020-08-20
Category : Mathematics
ISBN : 9783030537258

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Geometric Analysis by Ailana Fraser,André Neves,Peter M. Topping,Paul C. Yang Pdf

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.

Geometric and Topological Inference

Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
Geometric and Topological Inference Book PDF

Author : Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
Publisher : Cambridge University Press
Page : 247 pages
File Size : 52,5 Mb
Release : 2018-09-27
Category : Computers
ISBN : 9781108419390

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Geometric and Topological Inference by Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec Pdf

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Methods of Geometric Analysis in Extension and Trace Problems

Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd
Methods of Geometric Analysis in Extension and Trace Problems Book PDF

Author : Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd
Publisher : Springer Science & Business Media
Page : 560 pages
File Size : 47,5 Mb
Release : 2011-10-07
Category : Mathematics
ISBN : 9783034802093

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Methods of Geometric Analysis in Extension and Trace Problems by Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd Pdf

The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.

Functional and Shape Data Analysis

Anuj Srivastava,Eric P. Klassen
Functional and Shape Data Analysis Book PDF

Author : Anuj Srivastava,Eric P. Klassen
Publisher : Springer
Page : 447 pages
File Size : 46,6 Mb
Release : 2016-10-03
Category : Mathematics
ISBN : 9781493940202

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Functional and Shape Data Analysis by Anuj Srivastava,Eric P. Klassen Pdf

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.

Mathematical Foundations for Data Analysis

Jeff M. Phillips
Mathematical Foundations for Data Analysis Book PDF

Author : Jeff M. Phillips
Publisher : Springer Nature
Page : 299 pages
File Size : 49,9 Mb
Release : 2021-03-29
Category : Mathematics
ISBN : 9783030623418

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Mathematical Foundations for Data Analysis by Jeff M. Phillips Pdf

This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.

Geometric Analysis

Peter Li
Geometric Analysis Book PDF

Author : Peter Li
Publisher : Cambridge University Press
Page : 417 pages
File Size : 44,5 Mb
Release : 2012-05-03
Category : Mathematics
ISBN : 9781107020641

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Geometric Analysis by Peter Li Pdf

This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.

The Oxford Handbook of Pierre Bourdieu

Thomas Medvetz,Jeffrey J. Sallaz
The Oxford Handbook of Pierre Bourdieu Book PDF

Author : Thomas Medvetz,Jeffrey J. Sallaz
Publisher : Oxford University Press
Page : 696 pages
File Size : 54,6 Mb
Release : 2018-04-02
Category : Social Science
ISBN : 9780190874612

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The Oxford Handbook of Pierre Bourdieu by Thomas Medvetz,Jeffrey J. Sallaz Pdf

Pierre Bourdieu was one of the most influential social thinkers of the past half-century, known for both his theoretical and methodological contributions and his wide-ranging empirical investigations into colonial power in Algeria, the educational system in France, the forms of state power, and the history of artistic and scientific fields-among many other topics. Despite the depth and breadth of his influence, however, Bourdieu's legacy has yet to be assessed in a comprehensive manner. The Oxford Handbook of Pierre Bourdieu fills this gap by offering a sweeping overview of Bourdieu's impact on the social sciences and humanities. Thomas Medvetz and Jeffrey J. Sallaz have gathered a diverse array of leading scholars who place Bourdieu's work in the wider scope of intellectual history, trace the development of his thought, offer original interpretations and critical engagement, and discuss the likely impact of his ideas on future social research. The Handbook highlights Bourdieu's contributions to established areas of research-including the study of markets, the law, cultural production, and politics-and illustrates how his concepts have generated new fields and objects of study.