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Mixture Models in Forward Search Methods for Outlier Detection

  • Daniela G. Calò
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Forward search (FS) methods have been shown to be usefully employed for detecting multiple outliers in continuous multivariate data (Hadi, (1994); Atkinson et al., (2004)). Starting from an outlier-free subset of observations, they iteratively enlarge this good subset using Mahalanobis distances based only on the good observations. In this paper, an alternative formulation of the FS paradigm is presented, that takes a mixture of K > 1 normal components as a null model. The proposal is developed according to both the graphical and the inferential approach to FS-based outlier detection. The performance of the method is shown on an illustrative example and evaluated on a simulation experiment in the multiple cluster setting.

Keywords

Mixture Model Mahalanobis Distance Outlier Detection Forward Search Outlier Detection Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. ATKINSON, A.C. (1993): Stalactite plots and robust estimation for the detection of multivari-ate outliers. In: E. Ronchetti, E. Morgenthaler, and W. Stahel (Eds.): New Directions in Statistical Data Analysis and Robustenss., Birkhäuser, Basel.Google Scholar
  2. ATKINSON, A.C., RIANI, C. and CERIOLI A. (2004): Exploring Multivariate Data with the Forward Search. Springer, New York.zbMATHGoogle Scholar
  3. FRALEY, C. and RAFTERY, A.E. (1998): How may clusters? Which clustering method? Answers via model-based cluster analysis. The Computer Journal, 41, 578-588.zbMATHCrossRefGoogle Scholar
  4. HADI, A.S. (1994): A modification of a method for the detection of outliers in multivariate samples. J R Stat Soc, Ser B, 56, 393-396.zbMATHGoogle Scholar
  5. HARDIN, J. and ROCKE D.M. (2004): Outlier detection in the multiple cluster setting us-ing the minimum covariance determinant estimator. Computational Statistics and Data Analysis, 44, 625-638.CrossRefMathSciNetGoogle Scholar
  6. HENNIG, C. (2004): Breakdown point for maximum likelihood estimators of location-scale mixtures. The Annals of Statistics, 32, 1313-1340.zbMATHCrossRefMathSciNetGoogle Scholar
  7. MCLACHLAN, G.J. and BASFORD K.E. (1988): Mixture Models: Inference and Applica-tions to Clustering. Marcel Dekker, New York.Google Scholar
  8. MCLACHLAN, G.J. and PEEL, D. (2000): Finite Mixture Models. Wiley, New York.zbMATHCrossRefGoogle Scholar
  9. WANG S. et al. (1997): A new test for outlier detection from a multivariate mixture distribu-tion, Journal of Computational and Graphical Statistics, 6, 285-299.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Daniela G. Calò
    • 1
  1. 1.Department of StatisticsUniversity of BolognaBolognaItaly

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