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AuthorTitleYearJournal/ProceedingsReftypeDOI/URL
Dhillon, I. S., Modha, D. S. & Spangler, W. S. Class visualization of high-dimensional data with applications 2002 Computational Statistics & Data Analysis   article URL  
Abstract: No abstract is available for this item.
BibTeX:
@article{RePEc:eee:csdana:v:41:y:2002:i:1:p:59-90,
  author = {Dhillon, Inderjit S. and Modha, Dharmendra S. and Spangler, W. Scott},
  title = {Class visualization of high-dimensional data with applications},
  journal = {Computational Statistics \& Data Analysis},
  year = {2002},
  volume = {41},
  number = {1},
  pages = {59-90},
  url = {http://www.cs.utexas.edu/~inderjit/public_papers/csda.pdf}
}
Bezdek, J. C., Li, W. Q., Attikiouzel, Y. & Windham, M. A geometric approach to cluster validity for normal mixtures 1997 Soft Computing - A Fusion of Foundations, Methodologies and Applications   article URL  
Abstract: We study indices for choosing the correct number of components in a mixture of normal distributions. Previous studies have been confined to indices based wholly on probabilistic models. Viewing mixture decomposition as probabilistic clustering (where the emphasis is on partitioning for geometric substructure) as opposed to parametric estimation enables us to introduce both fuzzy and crisp measures of cluster validity for this problem. We presume the underlying samples to be unlabeled, and use the expectation-maximization (EM) algorithm to find clusters in the data. We test 16 probabilistic, 3 fuzzy and 4 crisp indices on 12 data sets that are samples from bivariate normal mixtures having either 3 or 6 components. Over three run averages based on different initializations of EM, 10 of the 23 indices tested for choosing the right number of mixture components were correct in at least 9 of the 12 trials. Among these were the fuzzy index of Xie-Beni, the crisp Davies-Bouldin index, and two crisp indices that are recent generalizations of Dunn's index.
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BibTeX:
@article{bezdek1997,
  author = {Bezdek, J. C. and Li, W. Q. and Attikiouzel, Y. and Windham, M.},
  title = {A geometric approach to cluster validity for normal mixtures},
  journal = {Soft Computing - A Fusion of Foundations, Methodologies and Applications},
  year = {1997},
  volume = {1},
  number = {4},
  pages = {166--179},
  url = {http://dx.doi.org/10.1007/s005000050019}
}
Kaufman, L. & Rousseeuw, P. J. Finding Groups in Data: An Introduction to Cluster Analysis 1990   book  
BibTeX:
@book{kaufman1990finding,
  author = {Kaufman, L. and Rousseeuw, P. J.},
  title = {Finding Groups in Data: An Introduction to Cluster Analysis},
  publisher = {John Wiley},
  year = {1990}
}
Rand, W. Objective criteria for the evaluation of clustering methods 1971 Journal of the American Statistical Association   article  
BibTeX:
@article{rand1971,
  author = {Rand, W.M.},
  title = {Objective criteria for the evaluation of clustering methods},
  journal = {Journal of the American Statistical Association },
  year = {1971},
  volume = {66},
  number = {336},
  pages = {846-850}
}

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