Induced Matchings of Barcodes and the Algebraic Stability of Persistence

@inproceedings{Bauer2014InducedMO,
  title={Induced Matchings of Barcodes and the Algebraic Stability of Persistence},
  author={Ulrich Bauer and Michael Lesnick},
  booktitle={Symposium on Computational Geometry},
  year={2014}
}
We define a simple, explicit map sending a morphism f: M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f. As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of… CONTINUE READING

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