000 02228cam a22002538i 4500
001 136735
003 ISI Library, Kolkata
005 20160407152147.0
008 150810s2015 riu b 001 0 eng
020 _a9781470425456 (alk. paper)
040 _aISI Library
_beng
082 0 4 _a510MS
_223
_bAm512
100 1 _aOudot, Steve Y.
245 1 0 _aPersistence theory : from quiver representations to data analysis /
_cSteve Y. Oudot.
260 _aProvidence :
_bAmerican Mathematical Society,
_c2015.
300 _aviii, 218 p. :
_billustrations (some color) ;
_c26 cm.
490 0 _aMathematical surveys and monographs ;
_vv 209.
504 _aIncludes bibliographical references and index.
505 0 _aPart 1. Theoretical foundations: 1. Algebraic persistence -- 2. Topological persistence -- 3. Stability -- Part 2. Applications: 4. Topological inference -- 5. Topological inference 2.0 -- 6. Clustering -- 7. Signatures for metric spaces -- Part 3. Perspectives: 8. New trends in topological data analysis -- 9. Further prospects on the theory -- Appendix A. Introduction to quiver theory with a view toward persistence -- Bibliography -- List of figures -- Index.
520 _a"Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organizaed into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis"--Back cover.
650 0 _aAlgebraic topology.
650 0 _aHomology theory.
942 _2ddc
_cBK
999 _c420765
_d420765