Optimally weighted L2 distance for functional data

Huaihou Chen, Philip T. Reiss, Thaddeus Tarpey

Research output: Contribution to journalArticlepeer-review


Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L2 distance. In this article we show that using a weighted L2 distance, with a judiciously chosen weight function, can improve the performance of various statistical methods for functional data, including k-medoids clustering, nonparametric classification, and permutation testing. Assuming a quadratically penalized (e.g., spline) basis representation for the functional data, we consider three nontrivial weight functions: design density weights, inverse-variance weights, and a new weight function that minimizes the coefficient of variation of the resulting squared distance by means of an efficient iterative procedure. The benefits of weighting, in particular with the proposed weight function, are demonstrated both in simulation studies and in applications to the Berkeley growth data and a functional magnetic resonance imaging data set.

Original languageEnglish
Pages (from-to)516-525
Number of pages10
Issue number3
StatePublished - 1 Sep 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, The International Biometric Society.


  • Coefficient of variation
  • Functional classification
  • Functional clustering
  • Penalized splines
  • Weighted L2 distance

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Statistics and Probability


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