Stability of Persistence Diagrams
- First Online:
- Cite this article as:
- Cohen-Steiner, D., Edelsbrunner, H. & Harer, J. Discrete Comput Geom (2007) 37: 103. doi:10.1007/s00454-006-1276-5
- 687 Downloads
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.