D. Cohen-Steiner, H. Edelsbrunner, J. Harer
tlooto Summary
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane and it is proved that under mild assumptions on the function, the persistence diagram is stable.
Abstract
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.
Citation format
COHEN-STEINER, D.; EDELSBRUNNER, H.; HARER, J. Stability of persistence diagrams. DISCRETE & COMPUTATIONAL GEOMETRY, 2005, 37: 103–120.