@article{3972, 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.}, author = {Cohen-Steiner, David and Herbert Edelsbrunner and Harer, John}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {103 -- 120}, publisher = {Springer}, title = {{Stability of persistence diagrams}}, doi = {10.1007/s00454-006-1276-5}, volume = {37}, year = {2007}, }