Dhillon,InderjitS.
Modha,DharmendraS.
Spangler,W.Scott
Class visualization of high-dimensional data with applications
Computational Statistics & Data Analysis
41
59-90
2002
No abstract is available for this item.
Bezdek,J.C.
Li,W.Q.
Attikiouzel,Y.
Windham,M.
A geometric approach to cluster validity for normal mixtures
Soft Computing - A Fusion of Foundations, Methodologies and Applications
1
166–179
1997
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.
ER -
Kaufman,L.
Rousseeuw,P.J.
Finding Groups in Data: An Introduction to Cluster Analysis
John Wiley
1990
Rand,W.M.
Objective criteria for the evaluation of clustering methods
Journal of the American Statistical Association
66
846-850
1971