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A stable cardinality distance for topological classification

Author

Listed:
  • Vasileios Maroulas

    (University of Tennessee)

  • Cassie Putman Micucci

    (University of Tennessee)

  • Adam Spannaus

    (University of Tennessee)

Abstract

This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on the space of persistence diagrams generates relevant input features for a classification algorithm for materials science data. This distance measures the similarity of persistence diagrams using the cost of matching points and a regularization term corresponding to cardinality differences between diagrams. Establishing stability properties of this distance provides theoretical justification for the use of the distance in comparisons of such diagrams. The classification scheme succeeds in determining the crystal structure of materials on noisy and sparse data retrieved from synthetic atom probe tomography experiments.

Suggested Citation

  • Vasileios Maroulas & Cassie Putman Micucci & Adam Spannaus, 2020. "A stable cardinality distance for topological classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 611-628, September.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:3:d:10.1007_s11634-019-00378-3
    DOI: 10.1007/s11634-019-00378-3
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    References listed on IDEAS

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    1. Andrew Marchese & Vasileios Maroulas, 2018. "Signal classification with a point process distance on the space of persistence diagrams," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 657-682, September.
    2. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    3. Angelo Ziletti & Devinder Kumar & Matthias Scheffler & Luca M. Ghiringhelli, 2018. "Insightful classification of crystal structures using deep learning," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
    4. Mathieu Carrière & Marco Cuturi & Steve Oudot, 2017. "Sliced Wasserstein Kernel for Persistence Diagrams," Working Papers 2017-82, Center for Research in Economics and Statistics.
    5. Louis J. Santodonato & Yang Zhang & Mikhail Feygenson & Chad M. Parish & Michael C. Gao & Richard J.K. Weber & Joerg C Neuefeind & Zhi Tang & Peter K Liaw, 2015. "Deviation from high-entropy configurations in the atomic distributions of a multi-principal-element alloy," Nature Communications, Nature, vol. 6(1), pages 1-13, May.
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