Corpus ID: 224705357

Stability of 2-Parameter Persistent Homology

@article{Blumberg2020StabilityO2,
  title={Stability of 2-Parameter Persistent Homology},
  author={Andrew J. Blumberg and Michael Lesnick},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.09628}
}
The \v{C}ech and Rips constructions of persistent homology are stable with respect to perturbations of the input data. However, neither is robust to outliers, and both can be insensitive to topological structure of high-density regions of the data. A natural solution is to consider 2-parameter persistence. This paper studies the stability of 2-parameter persistent homology: We show that several related density-sensitive constructions of bifiltrations from data satisfy stability properties… Expand

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