A probabilistic method for detecting multivariate extreme outliers

Shafiu Jibrin, Irwin S. Pressman, Matias Salibian-Barrera

Research output: Contribution to journalArticlepeer-review


Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.

Original languageEnglish (US)
Pages (from-to)157-170
Number of pages14
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Issue number2
StatePublished - 2004


  • D-optimal design
  • Extreme outliers
  • Monte Carlo
  • Outlierness
  • Redundancy
  • Semidefinite programming

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Modeling and Simulation
  • Engineering (miscellaneous)
  • Mechanics of Materials
  • General Physics and Astronomy
  • Applied Mathematics


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