Mathematical Principles Of Topological And Geometric Data Analysis PDF Download
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Author | : Parvaneh Joharinad |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : 9783031334412 |
Download Mathematical Principles of Topological and Geometric Data Analysis Book in PDF, ePub and Kindle
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.
Author | : Parvaneh Joharinad |
Publisher | : Springer Nature |
Total Pages | : 287 |
Release | : 2023-07-29 |
Genre | : Mathematics |
ISBN | : 303133440X |
Download Mathematical Principles of Topological and Geometric Data Analysis Book in PDF, ePub and Kindle
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.
Author | : Tamal Krishna Dey |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 2022-03-10 |
Genre | : Mathematics |
ISBN | : 1009103199 |
Download Computational Topology for Data Analysis Book in PDF, ePub and Kindle
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.
Author | : Jean-Daniel Boissonnat |
Publisher | : Cambridge University Press |
Total Pages | : 247 |
Release | : 2018-09-27 |
Genre | : Computers |
ISBN | : 1108419399 |
Download Geometric and Topological Inference Book in PDF, ePub and Kindle
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Author | : Gunnar Carlsson |
Publisher | : Cambridge University Press |
Total Pages | : 233 |
Release | : 2021-12-16 |
Genre | : Computers |
ISBN | : 1108838650 |
Download Topological Data Analysis with Applications Book in PDF, ePub and Kindle
This timely text introduces topological data analysis from scratch, with detailed case studies.
Author | : Tamal Krishna Dey |
Publisher | : Cambridge University Press |
Total Pages | : 455 |
Release | : 2022-03-10 |
Genre | : Computers |
ISBN | : 1009098160 |
Download Computational Topology for Data Analysis Book in PDF, ePub and Kindle
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Author | : Fred H. Croom |
Publisher | : Courier Dover Publications |
Total Pages | : 340 |
Release | : 2016-02-17 |
Genre | : Mathematics |
ISBN | : 0486801543 |
Download Principles of Topology Book in PDF, ePub and Kindle
Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.
Author | : Raúl Rabadán |
Publisher | : Cambridge University Press |
Total Pages | : 521 |
Release | : 2019-10-31 |
Genre | : Science |
ISBN | : 1108753396 |
Download Topological Data Analysis for Genomics and Evolution Book in PDF, ePub and Kindle
Biology has entered the age of Big Data. The technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce questions to a comparison of algebraic invariants, such as numbers, which are typically easier to solve. Topological data analysis is a rapidly-developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology alongside mathematicians interested in applied topology.
Author | : Hal Schenck |
Publisher | : Springer Nature |
Total Pages | : 231 |
Release | : 2022-11-21 |
Genre | : Mathematics |
ISBN | : 3031066642 |
Download Algebraic Foundations for Applied Topology and Data Analysis Book in PDF, ePub and Kindle
This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience. The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user’s guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field. Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.
Author | : Hamish Carr |
Publisher | : Springer Nature |
Total Pages | : 264 |
Release | : 2020-12-10 |
Genre | : Mathematics |
ISBN | : 3030430367 |
Download Topological Methods in Data Analysis and Visualization V Book in PDF, ePub and Kindle
This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.