Corpus ID: 19807367

Sliced Wasserstein Kernel for Persistence Diagrams

@inproceedings{Carrire2017SlicedWK,
  title={Sliced Wasserstein Kernel for Persistence Diagrams},
  author={Mathieu Carri{\`e}re and Marco Cuturi and S. Oudot},
  booktitle={ICML},
  year={2017}
}
  • Mathieu Carrière, Marco Cuturi, S. Oudot
  • Published in ICML 2017
  • Computer Science, Mathematics
  • Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endowed with a Hilbert structure and are usually compared with non-Hilbertian distances, such as the bottleneck distance. To incorporate PDs in a convex learning pipeline, several… CONTINUE READING
    117 Citations
    Persistence Fisher Kernel : A Riemannian Manifold Kernel for Persistence Diagrams
    • 8
    • Highly Influenced
    • PDF
    Persistence Fisher Kernel : A Riemannian Manifold Kernel for Persistence Diagrams
    • Highly Influenced
    • PDF
    On the Metric Distortion of Embedding Persistence Diagrams into Separable Hilbert Spaces
    • 11
    • PDF
    Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport
    • 23
    • PDF
    Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams
    • 19
    • Highly Influenced
    • PDF
    Wasserstein Stability for Persistence Diagrams
    • 3
    • PDF
    Persistence Curves: A canonical framework for summarizing persistence diagrams
    • 12
    • PDF
    On the choice of weight functions for linear representations of persistence diagrams
    • 16
    • PDF
    PersLay: A Simple and Versatile Neural Network Layer for Persistence Diagrams
    • 6

    References

    SHOWING 1-10 OF 53 REFERENCES
    Statistical Topological Data Analysis - A Kernel Perspective
    • 47
    • PDF
    Proximity of persistence modules and their diagrams
    • 333
    • PDF
    Kernel Method for Persistence Diagrams via Kernel Embedding and Weight Factor
    • 44
    • PDF
    Persistence Images: A Stable Vector Representation of Persistent Homology
    • 231
    • Highly Influential
    • PDF
    Sliced Wasserstein Kernels for Probability Distributions
    • 68
    • PDF
    Persistence weighted Gaussian kernel for topological data analysis
    • 102
    • Highly Influential
    • PDF
    Statistical topological data analysis using persistence landscapes
    • Peter Bubenik
    • Mathematics, Computer Science
    • J. Mach. Learn. Res.
    • 2015
    • 390
    • PDF