A Stable Cardinality Distance for Topological Classification

@article{Maroulas2018ASC,
  title={A Stable Cardinality Distance for Topological Classification},
  author={Vasileios Maroulas and Cassie Putman Micucci and Adam Spannaus},
  journal={ArXiv},
  year={2018},
  volume={abs/1812.01664}
}
  • Vasileios Maroulas, Cassie Putman Micucci, Adam Spannaus
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • This work incorporates topological and geometric features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are planar sets that summarize the shape details of given data. A new metric on persistence diagrams generates input features for the classification algorithm. The metric accounts for the similarity of persistence diagrams using a linear combination of matching costs and cardinality differences. Investigation of the stability… CONTINUE READING

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 48 REFERENCES

    Κ-means clustering on the space of persistence diagrams

    VIEW 1 EXCERPT

    Statistical topological data analysis using persistence landscapes

    • Peter Bubenik
    • Computer Science, Mathematics
    • J. Mach. Learn. Res.
    • 2015
    VIEW 1 EXCERPT

    Persistence Images: A Stable Vector Representation of Persistent Homology

    VIEW 1 EXCERPT

    Geometry Helps to Compare Persistence Diagrams

    VIEW 1 EXCERPT

    Object-oriented persistent homology

    • B. Wang, G. Wei
    • Mathematics, Medicine, Computer Science
    • J. Comput. Phys.
    • 2016
    VIEW 1 EXCERPT

    Topological persistence and simplification

    VIEW 1 EXCERPT

    Stability of persistence diagrams

    VIEW 2 EXCERPTS