Lattice Paths for Persistent Diagrams

@article{Chung2021LatticePF,
  title={Lattice Paths for Persistent Diagrams},
  author={Moo K. Chung and Hernando C. Ombao},
  journal={Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data : 4th International Workshop, iMIMIC 2021, and 1st International Workshop, TDA4MedicalData 2021, He...},
  year={2021},
  volume={12929},
  pages={
          77-86
        }
}
  • Moo K. Chung, H. Ombao
  • Published 1 May 2021
  • Mathematics
  • Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data : 4th International Workshop, iMIMIC 2021, and 1st International Workshop, TDA4MedicalData 2021, He...
Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path representation for persistent diagrams. We then develop a new exact statistical inference procedure for lattice paths via combinatorial enumerations. The lattice path method is applied to the topological characterization of the protein structures of the COVID… 

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