Quasi-interpolation and outliers removal

Anat Amir*, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this work, we present a method that will allow us to remove outliers from a data set. Given the measurements of a function f = g + e on a set of sample points X⊂ ℝd, where g∈ CM+1(ℝd) is the function of interest and e is the deviation from the function g. We will say that a sample point x ∈ X is an outlier if the difference e(x) = f(x) − g(x) is large. We show that by analyzing the approximation errors on our sample set X, we may predict which of the sample points are outliers. Furthermore, we can identify outliers of very small deviations, as well as ones with large deviations.

Original languageEnglish
Pages (from-to)805-825
Number of pages21
JournalNumerical Algorithms
Issue number3
StatePublished - 1 Jul 2018


  • Moving least squares
  • Multivariate approximation
  • Outliers


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