Discrete topological methods for cybersecurity, network science, and machine learning

Steve Huntsman (1)

1 Systems and Technology Research

This is an advertisement for (or a rant about) discrete topological methods-fairly new even by the standards of topological data analysis, and certainly underutilized at present-that are naturally suited to analyze (hyper)graphical data prevalent in cybersecurity applications, network science, and tasks in machine learning. As outstanding exemplars in this vein, we briefly discuss path homology and magnitude homology before paying lip service to sheaves, curvatures, and geodesics in discrete settings. Throughout, we mention new or plausible near-term applications.

Mots clés: topological data analysis; Dowker homology; path homology; magnitude homology AMS subject classifications. 55N31; 55N35; 55U05; topological data analysis

Domaines: Topologie algébrique [math.AT]

Steve Huntsman. Discrete topological methods for cybersecurity, network science, and machine learning. 2022. ⟨hal-03688966⟩