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Topological data analysis with applications /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Topological data analysis with applications /Gunnar Carlsson, Mikael Vejdemo-Johansson.
Author:	Carlsson, G.
other author:	Vejdemo-Johansson, Mikael,
Description:	xi, 220 pages :illustrations (some color) ;26 cm
Subject:	Topology.
ISBN:	9781108838658

Topological data analysis with applications /
Carlsson, G.1952-

Topological data analysis with applications /Gunnar Carlsson, Mikael Vejdemo-Johansson. - xi, 220 pages :illustrations (some color) ;26 cm

Includes bibliographical references (pages 207-215) and index.

Part I: Background. Introduction. Overview -- Examples of qualitative properties in applications -- Data. Data matrices and spreadsheets -- Dissimilarity matrices and metrics -- Categorical data and sequences -- Text -- Graph data -- Images -- Time series -- Density estimation in point cloud data -- Part II: Theory. Topology. History -- Qualitative and quantitative properties -- Chain complexes and homology -- Shape of data. Zero-dimensional topology: single-linkage clustering -- The nerve construction and soft clustering -- Complexes for point cloud data -- Persistence -- The algebra of persistence vector spaces -- Persistence and localization of features -- Non-homotopy-invariant shape recognition -- Zig-zag persistence -- Multidimensional persistence -- Structures on spaces of barcodes. Metrics on barcode spaces -- Coordinatizing barcode space and feature generation -- Distributions on B -- Part III: Practice. Case studies. Mumford natural image data -- Databases of compounds -- Viral evolution -- Time series -- Sensor coverage and evasion -- Vectorization methods and machine learning -- Caging grasps -- Structure of the cosmic web -- Politics -- Amorphous solids -- Infectious diseases

"The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higherdimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used"--

ISBN: 9781108838658

LCCN: 2021024970

Nat. Bib. No.: GBC1H9893bnb

Nat. Bib. Agency Control No.: 020378184UkSubjects--Topical Terms:

185965
Topology.

LC Class. No.: QA611 / .C29 2022

Dewey Class. No.: 514/.23

Topological data analysis with applications /
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020 $z 9781108975704 $q electronic book
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082 0 0 $a 514/.23 $2 23
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100 1 $a Carlsson, G. $q (Gunnar), $d 1952- $e author. $3 916213
245 1 0 $a Topological data analysis with applications / $c Gunnar Carlsson, Mikael Vejdemo-Johansson.
264 1 $a Cambridge, United Kingdom ; $a New York, NY : $b Cambridge University Press, $c 2022.
264 4 $c ©2022
300 $a xi, 220 pages : $b illustrations (some color) ; $c 26 cm
336 $a text $b txt $2 rdacontent
337 $a unmediated $b n $2 rdamedia
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504 $a Includes bibliographical references (pages 207-215) and index.
505 0 $a Part I: Background. Introduction. Overview -- Examples of qualitative properties in applications -- Data. Data matrices and spreadsheets -- Dissimilarity matrices and metrics -- Categorical data and sequences -- Text -- Graph data -- Images -- Time series -- Density estimation in point cloud data -- Part II: Theory. Topology. History -- Qualitative and quantitative properties -- Chain complexes and homology -- Shape of data. Zero-dimensional topology: single-linkage clustering -- The nerve construction and soft clustering -- Complexes for point cloud data -- Persistence -- The algebra of persistence vector spaces -- Persistence and localization of features -- Non-homotopy-invariant shape recognition -- Zig-zag persistence -- Multidimensional persistence -- Structures on spaces of barcodes. Metrics on barcode spaces -- Coordinatizing barcode space and feature generation -- Distributions on B -- Part III: Practice. Case studies. Mumford natural image data -- Databases of compounds -- Viral evolution -- Time series -- Sensor coverage and evasion -- Vectorization methods and machine learning -- Caging grasps -- Structure of the cosmic web -- Politics -- Amorphous solids -- Infectious diseases
520 $a "The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higherdimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used"-- $c Provided by publisher.
650 0 $a Topology. $3 185965
650 0 $a Mathematical analysis. $3 186133
650 6 $a Topologie. $2 gtt $3 272452
650 6 $a Analyse mathématique. $3 916307
650 7 $a MATHEMATICS / Topology. $2 bisacsh $3 916216
700 1 $a Vejdemo-Johansson, Mikael, $d 1980- $e author. $3 916214
776 0 8 $i ebook version : $z 9781108975704
938 $a YBP Library Services $b YANK $n 17429730
994 $a C0 $b TWNUK