Stability of Persistence Diagrams
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- Cohen-Steiner, D., Edelsbrunner, H. & Harer, J. Discrete Comput Geom (2007) 37: 103. doi:10.1007/s00454-006-1276-5
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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.