Stability of persistence diagrams
Authors:
Open Access
- 6 June 2005
- conference paper
- Published by Association for Computing Machinery (ACM)
- Vol. 37 (1) , 263-271
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.Keywords
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