Proximity of persistence modules and their diagrams

  title={Proximity of persistence modules and their diagrams},
  author={F. Chazal and D. Cohen-Steiner and M. Glisse and L. Guibas and S. Oudot},
  booktitle={SCG '09},
  • F. Chazal, D. Cohen-Steiner, +2 authors S. Oudot
  • Published in SCG '09 2009
  • Mathematics, Computer Science
  • Topological persistence has proven to be a key concept for the study of real-valued functions defined over topological spaces. Its validity relies on the fundamental property that the persistence diagrams of nearby functions are close. However, existing stability results are restricted to the case of continuous functions defined over triangulable spaces. In this paper, we present new stability results that do not suffer from the above restrictions. Furthermore, by working at an algebraic level… CONTINUE READING
    333 Citations

    Figures and Topics from this paper

    Higher Interpolation and Extension for Persistence Modules
    • 15
    • Highly Influenced
    • PDF
    Rank-based persistence
    • 2
    • PDF
    Geometry in the space of persistence modules
    • 5
    • PDF
    Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability
    • 8
    • Highly Influenced
    • PDF
    Hausdorff Stability of Persistence Spaces
    • 12
    Correspondence Modules and Persistence Sheaves: A Unifying Framework for One-Parameter Persistent Homology
    • Highly Influenced
    • PDF
    Stability of persistence spaces of vector-valued continuous functions
    • 4
    • PDF
    Algebraic Stability of Zigzag Persistence Modules
    • 49
    • PDF
    The Persistent Homotopy Type Distance
    • 10
    • PDF
    Topological spaces of persistence modules and their properties
    • 20
    • PDF


    Proximity of persistence modules and their diagrams
    • Research Report 6568,
    • 2008