Persistence theory : from quiver representations to data analysis / Steve Y. Oudot.

Format:

Book

Author/Creator:

Oudot, Steve Y., 1979- author.

Series:

Mathematical surveys and monographs ; Volume 209.

Mathematical Surveys and Monographs ; Volume 209

Language:

English

Subjects (All):

Algebraic topology.

Homology theory.

Physical Description:

1 online resource (220 pages) : illustrations.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2015.

Summary:

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.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-2795-8