A topic within Topology, itself one of 11 topics in that field and part of Mathematics.
Assumes you know the vocabulary.
Topology and Data
Gunnar Carlsson · 2009
Argues that the shape of high-dimensional data — its clusters, loops and voids — is a legitimate object of study in its own right, and adapts…
+1 more at this level
Primary sources and full treatments.
Persistent Homology - A Survey
Herbert Edelsbrunner & John Harer · 2008
Argues that persistence itself, not any single scale, is the right topological invariant of noisy data, laying out an algorithm that extracts robust…
3 works
Gunnar Carlsson
Argues that the shape of high-dimensional data — its clusters, loops and voids — is a legitimate object of study in its own right, and adapts homology to work on point clouds instead of manifolds.
link checked 17 Sept 2026Robert Ghrist
Argues that topology, not just calculus, is the natural mathematics of large-scale qualitative structure, building the case through persistent homology, sheaves and Euler calculus applied to sensor networks, signals and data.
link checked 17 Sept 2026Herbert Edelsbrunner & John Harer
Argues that persistence itself, not any single scale, is the right topological invariant of noisy data, laying out an algorithm that extracts robust components, loops and voids from a point cloud.
link checked 17 Sept 2026