Metrics for Learning in Topological Persistence

Henri Riihimaki* (Corresponding Author), José Licón Saláiz

*Corresponding author for this work

Research output: Contribution to conferenceUnpublished paperpeer-review

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Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can stabilize invariants characterizing these objects. We outline how so called contour functions induce relevant metrics for stabilizing the rank invariant. On the practical level, the stable ranks are used as fingerprints for data. Different choices of contour lead to different stable ranks and the topological learning is then the question of finding the optimal contour. We outline our analysis pipeline and show how it can enhance classification of physical activities data. As our main application we study how stable ranks and contours provide robust descriptors of spatial patterns of atmospheric cloud fields.
Original languageEnglish
Number of pages16
Publication statusPublished - 16 Sept 2019
EventApplications of Topological Data Analysis: International Workshop on Applications of Topological Data Analysis - Würzburg, Germany
Duration: 16 Sept 201916 Sept 2019


WorkshopApplications of Topological Data Analysis
Abbreviated titleATDA2019
Internet address

Bibliographical note

We gratefully acknowledge Roel Neggers for providing the DALES simulation
data. JLS acknowledges support by the DFG-funded transregional research
collaborative TR32 on Patterns in Soil–Vegetation–Atmosphere Systems.


  • Persistent homology
  • Topological learning
  • Stable rank
  • Atmospheric science


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