Persistence theory : from quiver representations to data analysis
著者
書誌事項
Persistence theory : from quiver representations to data analysis
（Mathematical surveys and monographs, v. 209）
American Mathematical Society, c2015
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注記
"Applied mathematics"--Cover
Includes bibliographical references (p. 197-212) and index
内容説明・目次
内容説明
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 persistence theory, 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 organized 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. It can be used as a text for a course on applied topology, on data analysis, or on applied statistics.
目次
Theoretical foundations: Algebraic persistence
Topological persistence
Stability Applications: Topological inference
Topological inference 2.0
Clustering Signatures for metric spaces
Perspectives: New trends in topological data analysis
Further prospects on the theory
Introduction to quiver theory with a view toward persistence
Bibliography
List of figures
Index
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