Introduction to Topological Data Analysis

Julien Tierny (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

This document introduces the key concepts and algorithms of Topological Data Analysis in low dimensions. First, the input data representation is formalized. Second, some of the core concepts of Topological Data Analysis are presented, including critical points, notions of Persistent Homology, Reeb graphs and Morse-Smale Complexes. Finally, a brief review of the state-of-the-art algorithms is presented. For the reader's convenience, the most important definitions and properties are highlighted with boxes. For further readings, I refer the reader to the excellent introduction to Computational Topology by Edelsbrunner and Harer.

Domaines: Informatique [cs]; Mathématiques [math]; Géométrie algorithmique [cs.CG]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Mathématique discrète [cs.DM]; Synthèse d'image et réalité virtuelle [cs.GR]; Logiciel mathématique [cs.MS]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Topologie générale [math.GN]

Julien Tierny. Introduction to Topological Data Analysis. Doctoral. France. 2017. ⟨cel-01581941⟩