Integrated shape-sensitive functional metrics

Sami Helander, Petra Laketa, Pauliina Ilmonen, Stanislav Nagy, Germain Van Bever, Lauri Viitasaari

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the Lp distance in general function spaces. Selecting d as the Hausdorff or Fréchet distances, we introduce integrated shape-sensitive versions of these supremum-based metrics. The new metrics allow for finer analyses in functional settings, not attainable applying the non-integrated versions directly. Moreover, convergent discrete approximations make computations feasible in practice.
Original languageEnglish
Article number104880
Number of pages14
JournalJournal of Multivariate Analysis
Early online date2021
Publication statusPublished - May 2022
MoE publication typeA1 Journal article-refereed


  • Fréchet distance
  • Functional data analysis
  • Hausdorff distance
  • Pseudometric


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