Persistence Theory: From Quiver Representations to Data Analysis

Steve Y. Oudot (1, 2)

1 GEOMETRICA - Geometric computing
2 DATASHAPE - Understanding the Shape of Data

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.

Domaines: Topologie algébrique [math.AT]; Géométrie algorithmique [cs.CG]

Steve Y. Oudot. Persistence Theory: From Quiver Representations to Data Analysis. American Mathematical Society, 209, pp.218, 2015, Mathematical Surveys and Monographs, 978-1-4704-2545-6. ⟨hal-01247501⟩