Metrics for Learning in Topological Persistence

Henri Riihimaki* (Corresponding Author), José Licón Saláiz

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

Abstract

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
DOIs
Publication statusPublished - 16 Sep 2019
EventApplications of Topological Data Analysis: International Workshop on Applications of Topological Data Analysis - Würzburg, Germany
Duration: 16 Sep 201916 Sep 2019
https://sites.google.com/view/atda2019/home

Workshop

WorkshopApplications of Topological Data Analysis
Abbreviated titleATDA2019
CountryGermany
CityWürzburg
Period16/09/1916/09/19
Internet address

Keywords

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

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