Persistence Theory - From Quiver Representations to Data Analysis

By Steve Y. Oudot. Mathematical Surveys and Monographs, 2015

426 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A roadmap for the computation of persistent homology (2015, background): “There are numerous excellent introductions to PH, such as the books [48, 59,100, 127] and the papers [21, 46, 47, 58].”
Toward unsupervised, multi-object discovery in large-scale image collections (2020, methodology): “Next, we find robust local maxima in the previous saliency map using persistence, a measure used in topological data analysis [5,8,9,25,41] to find critical points of a function (see Section 4.”
Decomposition of persistence modules (2018, background): “the survey by Carlsson [5], or the recent book by Oudot [12] on quiver representations and TDA.”
A Group-Theoretic Approach to Abstraction: Hierarchical, Interpretable, and Task-Free Clustering (2018, methodology): “In particular, greedy hierarchical clustering is oft-criticized since it is hard to recover from bad clusterings in early stages of construction (Oudot, 2015).”
Statistical Analysis and Parameter Selection for Mapper (2017, methodology): “All of them can be found, together with their proofs, in Dey and Wang (2013) and Carrière and Oudot (2015).”