Geometric Data Analysis

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Geometric Data Analysis

Author : Brigitte Le Roux
Publisher : Springer Science & Business Media
ISBN 13 : 1402022360
Total Pages : 475 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Geometric Data Analysis by : Brigitte Le Roux

Download or read book Geometric Data Analysis written by Brigitte Le Roux and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Brigitte Le Roux
Publisher : CRC Press
ISBN 13 : 1498781624
Total Pages : 256 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Combinatorial Inference in Geometric Data Analysis by : Brigitte Le Roux

Download or read book Combinatorial Inference in Geometric Data Analysis written by Brigitte Le Roux and published by CRC Press. This book was released on 2019-03-20 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Michael Kirby
Publisher : Wiley-Interscience
ISBN 13 : 9780471239291
Total Pages : 0 pages
Book Rating : 4.2/5 (392 download)

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Book Synopsis Geometric Data Analysis by : Michael Kirby

Download or read book Geometric Data Analysis written by Michael Kirby and published by Wiley-Interscience. This book was released on 2001-01-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorial Inference in Geometric Data Analysis

Author : Brigitte Le Roux
Publisher : CRC Press
ISBN 13 : 1351651331
Total Pages : 234 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Combinatorial Inference in Geometric Data Analysis by : Brigitte Le Roux

Download or read book Combinatorial Inference in Geometric Data Analysis written by Brigitte Le Roux and published by CRC Press. This book was released on 2019-03-20 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Structure of High-Dimensional Data and Dimensionality Reduction

Author : Jianzhong Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3642274978
Total Pages : 356 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Geometric Structure of High-Dimensional Data and Dimensionality Reduction by : Jianzhong Wang

Download or read book Geometric Structure of High-Dimensional Data and Dimensionality Reduction written by Jianzhong Wang and published by Springer Science & Business Media. This book was released on 2012-04-28 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Computational Topology for Data Analysis

Author : Tamal Krishna Dey
Publisher : Cambridge University Press
ISBN 13 : 1009103199
Total Pages : 456 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Computational Topology for Data Analysis by : Tamal Krishna Dey

Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.

Riemannian Geometric Statistics in Medical Image Analysis

Author : Xavier Pennec
Publisher : Academic Press
ISBN 13 : 0128147261
Total Pages : 636 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Riemannian Geometric Statistics in Medical Image Analysis by : Xavier Pennec

Download or read book Riemannian Geometric Statistics in Medical Image Analysis written by Xavier Pennec and published by Academic Press. This book was released on 2019-09-02 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Parvaneh Joharinad
Publisher :
ISBN 13 : 9783031334412
Total Pages : 0 pages
Book Rating : 4.3/5 (344 download)

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Book Synopsis Mathematical Principles of Topological and Geometric Data Analysis by : Parvaneh Joharinad

Download or read book Mathematical Principles of Topological and Geometric Data Analysis written by Parvaneh Joharinad and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Analysis

Author : Ailana Fraser
Publisher : Springer Nature
ISBN 13 : 3030537250
Total Pages : 146 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Geometric Analysis by : Ailana Fraser

Download or read book Geometric Analysis written by Ailana Fraser and published by Springer Nature. This book was released on 2020-08-20 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Foundations for Data Analysis

Author : Jeff M. Phillips
Publisher : Springer Nature
ISBN 13 : 3030623416
Total Pages : 299 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematical Foundations for Data Analysis by : Jeff M. Phillips

Download or read book Mathematical Foundations for Data Analysis written by Jeff M. Phillips and published by Springer Nature. This book was released on 2021-03-29 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Principles of Topological and Geometric Data Analysis

Author : Parvaneh Joharinad
Publisher : Springer Nature
ISBN 13 : 303133440X
Total Pages : 287 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Mathematical Principles of Topological and Geometric Data Analysis by : Parvaneh Joharinad

Download or read book Mathematical Principles of Topological and Geometric Data Analysis written by Parvaneh Joharinad and published by Springer Nature. This book was released on 2023-07-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Geometric Analysis in Extension and Trace Problems

Author : Alexander Brudnyi
Publisher : Springer Science & Business Media
ISBN 13 : 3034802099
Total Pages : 560 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Methods of Geometric Analysis in Extension and Trace Problems by : Alexander Brudnyi

Download or read book Methods of Geometric Analysis in Extension and Trace Problems written by Alexander Brudnyi and published by Springer Science & Business Media. This book was released on 2011-10-07 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric and Topological Inference

Author : Jean-Daniel Boissonnat
Publisher : Cambridge University Press
ISBN 13 : 1108419399
Total Pages : 247 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Geometric and Topological Inference by : Jean-Daniel Boissonnat

Download or read book Geometric and Topological Inference written by Jean-Daniel Boissonnat and published by Cambridge University Press. This book was released on 2018-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Functional and Shape Data Analysis

Author : Anuj Srivastava
Publisher : Springer
ISBN 13 : 1493940201
Total Pages : 447 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Functional and Shape Data Analysis by : Anuj Srivastava

Download or read book Functional and Shape Data Analysis written by Anuj Srivastava and published by Springer. This book was released on 2016-10-03 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Peter Li
Publisher : Cambridge University Press
ISBN 13 : 1107020646
Total Pages : 417 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Geometric Analysis by : Peter Li

Download or read book Geometric Analysis written by Peter Li and published by Cambridge University Press. This book was released on 2012-05-03 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.

Digital Geometry

Author : Reinhard Klette
Publisher : Elsevier
ISBN 13 : 0080477267
Total Pages : 672 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Digital Geometry by : Reinhard Klette

Download or read book Digital Geometry written by Reinhard Klette and published by Elsevier. This book was released on 2004-09-04 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision *Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data *Includes exercises, examples, and references to related or more advanced work

Vanishing and Finiteness Results in Geometric Analysis

Author : Stefano Pigola
Publisher : Springer Science & Business Media
ISBN 13 : 3764386428
Total Pages : 282 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Vanishing and Finiteness Results in Geometric Analysis by : Stefano Pigola

Download or read book Vanishing and Finiteness Results in Geometric Analysis written by Stefano Pigola and published by Springer Science & Business Media. This book was released on 2008-05-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.