Outlier Detection in High Dimension Using Regularization

  • Moritz GschwandtnerEmail author
  • Peter Filzmoser
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 190)


An outlier detection method for high dimensional data is presented in this paper. It makes use of a robust and regularized estimation of the covariance matrix which is achieved by maximization of a penalized version of the likelihood function for joint location and inverse scatter. A penalty parameter controls the amount of regularization.

The algorithm is computation intensive but provides higher efficiency than other methods. This fact will be demonstrated in an example with simulated data, in which the presented method is compared to another algorithm for high dimensional data.


Outliers regularization robust statistics 


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  1. 1.
    Croux, C., Gelper, S., Haesbroeck, G.: The regularized minimum covariance determinant estimator (preprint),
  2. 2.
    Croux, C., Haesbroeck, G.: Robust scatter regularization. Compstat, Book of Abstracts, Paris, Conservatoire National des Arts et Métiers (CNAM) and the French National Institute for Research in Computer Science and Control, INRIA (2010)Google Scholar
  3. 3.
    Filzmoser, P., Gschwandtner, M.: mvoutlier: Multivariate outlier detection based on robust methods. R package version 1.9.4 (2011)Google Scholar
  4. 4.
    Filzmoser, P., Maronna, R., Werner, M.: Outlier identification in high dimensions. Comput. Stat. Data An. 52, 1694–1711 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Friedman, J.H., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostat. 9, 432–441 (2007)CrossRefGoogle Scholar
  6. 6.
    Rousseeuw, P.J., Van Driessen, K.: A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212–223 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Statistics and Probability TheoryVienna University of TechnologyViennaAustria

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