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Algebraic foundations for applied to...

Schenck, Hal.

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Algebraic foundations for applied topology and data analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algebraic foundations for applied topology and data analysis/ by Hal Schenck.
作者:	Schenck, Hal.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xii, 224 p. :ill., digital ;24 cm.
內容註:	Preface -- 1. Linear Algebra Tools for Data Analysis -- 2. Basics of Algebra: Groups, Rings, Modules -- 3. Basics of Topology: Spaces and Sheaves -- 4. Homology I: Simplicial Complexes to Sensor Networks -- 5. Homology II: Cohomology to Ranking Problems -- 6. Persistent Algebra: Modules over a PID -- 7. Persistent Homology -- 8. Multiparameter Persistent Homology -- 9. Derived Functors and Spectral Sequences -- Appendix A. Examples of Software Packages -- Bibliography.
Contained By:	Springer Nature eBook
標題:	Algebraic topology. -
電子資源:	https://doi.org/10.1007/978-3-031-06664-1
ISBN:	9783031066641

Algebraic foundations for applied topology and data analysis
Schenck, Hal.

Algebraic foundations for applied topology and data analysis[electronic resource] /by Hal Schenck. - Cham :Springer International Publishing :2022. - xii, 224 p. :ill., digital ;24 cm. - Mathematics of data,v. 12731-4111 ;. - Mathematics of data ;v. 1..

Preface -- 1. Linear Algebra Tools for Data Analysis -- 2. Basics of Algebra: Groups, Rings, Modules -- 3. Basics of Topology: Spaces and Sheaves -- 4. Homology I: Simplicial Complexes to Sensor Networks -- 5. Homology II: Cohomology to Ranking Problems -- 6. Persistent Algebra: Modules over a PID -- 7. Persistent Homology -- 8. Multiparameter Persistent Homology -- 9. Derived Functors and Spectral Sequences -- Appendix A. Examples of Software Packages -- Bibliography.

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.

ISBN: 9783031066641

Standard No.: 10.1007/978-3-031-06664-1doiSubjects--Topical Terms:

532744
Algebraic topology.

LC Class. No.: QA612

Dewey Class. No.: 514.2

Algebraic foundations for applied topology and data analysis
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505 0 $a Preface -- 1. Linear Algebra Tools for Data Analysis -- 2. Basics of Algebra: Groups, Rings, Modules -- 3. Basics of Topology: Spaces and Sheaves -- 4. Homology I: Simplicial Complexes to Sensor Networks -- 5. Homology II: Cohomology to Ranking Problems -- 6. Persistent Algebra: Modules over a PID -- 7. Persistent Homology -- 8. Multiparameter Persistent Homology -- 9. Derived Functors and Spectral Sequences -- Appendix A. Examples of Software Packages -- Bibliography.
520 $a 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.
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