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Signal classification with a point process distance on the space of persistence diagrams

Author

Listed:
  • Andrew Marchese

    (University of Tennessee)

  • Vasileios Maroulas

    (University of Tennessee)

Abstract

In this paper, we consider the problem of signal classification. First, the signal is translated into a persistence diagram through the use of delay-embedding and persistent homology. Endowing the data space of persistence diagrams with a metric from point processes, we show that it admits statistical structure in the form of Fréchet means and variances and a classification scheme is established. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and changes in cardinality. The classification results using this distance are benchmarked on both synthetic data and real acoustic signals and it is demonstrated that this classifier outperforms current signal classification techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:3:d:10.1007_s11634-017-0294-x
    DOI: 10.1007/s11634-017-0294-x
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    Cited by:

    1. 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.

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