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On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

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  • McLachlan, G. J.
  • Khan, N.

Abstract

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 90 (2004)
Issue (Month): 1 (July)
Pages: 90-105

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Handle: RePEc:eee:jmvana:v:90:y:2004:i:1:p:90-105

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Keywords: Microarray gene expression data Mixture models Clustering of tissue samples Tests on number of clusters Likelihood ratio statistic Resampling approach;

References

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  1. 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, Elsevier, vol. 31(1), pages 1-11, July.
  2. J. Hartigan, 1985. "Statistical theory in clustering," Journal of Classification, Springer, Springer, vol. 2(1), pages 63-76, December.
  3. Allison, David B. & Gadbury, Gary L. & Heo, Moonseong & Fernandez, Jose R. & Lee, Cheol-Koo & Prolla, Tomas A. & Weindruch, Richard, 2002. "A mixture model approach for the analysis of microarray gene expression data," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 39(1), pages 1-20, March.
  4. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 41(3-4), pages 379-388, January.
  5. Huber Wolfgang & von Heydebreck Anja & Sueltmann Holger & Poustka Annemarie & Vingron Martin, 2003. "Parameter estimation for the calibration and variance stabilization of microarray data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, De Gruyter, vol. 2(1), pages 1-24, April.
  6. 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.
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Citations

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Cited by:
  1. Mark Chiang & Boris Mirkin, 2010. "Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads," Journal of Classification, Springer, Springer, vol. 27(1), pages 3-40, March.
  2. Wong, Tony Siu Tung & Li, Wai Keung, 2014. "Test for homogeneity in gamma mixture models using likelihood ratio," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 70(C), pages 127-137.
  3. Polymenis, Athanase, 2014. "A combined likelihood ratio/information ratio bootstrap technique for estimating the number of components in finite mixtures," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 71(C), pages 107-115.

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