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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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.
ATKINSON, A.C., RIANI, C. and CERIOLI A. (2004): Exploring Multivariate Data with the Forward Search. Springer, New York.
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.
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.
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.
HENNIG, C. (2004): Breakdown point for maximum likelihood estimators of location-scale mixtures. The Annals of Statistics, 32, 1313-1340.
MCLACHLAN, G.J. and BASFORD K.E. (1988): Mixture Models: Inference and Applica-tions to Clustering. Marcel Dekker, New York.
MCLACHLAN, G.J. and PEEL, D. (2000): Finite Mixture Models. Wiley, New York.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Calò, D.G. (2008). Mixture Models in Forward Search Methods for Outlier Detection. In: Preisach, C., Burkhardt, H., Schmidt-Thieme, L., Decker, R. (eds) Data Analysis, Machine Learning and Applications. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78246-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-78246-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78239-1
Online ISBN: 978-3-540-78246-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)