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Algebraic Foundations for Applied Topology and Data Analysis
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Algebraic Foundations for Applied Topology and Data Analysis/ by Hal Schenck.
作者:
Schenck, Hal.
面頁冊數:
XII, 224 p. 1 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Symbolic and Algebraic Manipulation. -
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. - 1st ed. 2022. - XII, 224 p. 1 illus.online resource. - Mathematics of Data,12731-4111 ;. - Mathematics of Data,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:
669944
Symbolic and Algebraic Manipulation.
LC Class. No.: QA612-612.8
Dewey Class. No.: 514.2
Algebraic Foundations for Applied Topology and Data Analysis
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