Using combinatorial optimization in model-based trimmed clustering with cardinality constraints
Statistical clustering criteria with free scale parameters and unknown cluster sizes are inclined to create small, spurious clusters. To mitigate this tendency a statistical model for cardinality-constrained clustering of data with gross outliers is established, its maximum likelihood and maximum a posteriori clustering criteria are derived, and their consistency and robustness are analyzed. The criteria lead to constrained optimization problems that can be solved by using iterative, alternating trimming algorithms of k-means type. Each step in the algorithms requires the solution of a [lambda]-assignment problem known from combinatorial optimization. The method allows one to estimate the numbers of clusters and outliers. It is illustrated with a synthetic data set and a real one.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
- Woodruff, David L. & Reiners, Torsten, 2004. "Experiments with, and on, algorithms for maximum likelihood clustering," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 237-253, September.
- Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer, vol. 50(2), pages 159-179, June.
- Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
- Coleman, Dan & Dong, Xioapeng & Hardin, Johanna & Rocke, David M. & Woodruff, David L., 1999. "Some computational issues in cluster analysis with no a priori metric," Computational Statistics & Data Analysis, Elsevier, vol. 31(1), pages 1-11, July.
- Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
- H. Bock, 1985. "On some significance tests in cluster analysis," Journal of Classification, Springer, vol. 2(1), pages 77-108, December.
- Baibing Li, 2006. "A new approach to cluster analysis: the clustering-function-based method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 457-476.
- María Gallegos & Gunter Ritter, 2009. "Trimming algorithms for clustering contaminated grouped data and their robustness," Advances in Data Analysis and Classification, Springer, vol. 3(2), pages 135-167, September.
- Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2004. "Testing for a finite mixture model with two components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 95-115.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:3:p:637-654. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.