Improved Criteria for Clustering Based on the Posterior Similarity Matrix Export

@article{citeulike:5387265, abstract = {In this paper we address the problem of obtaining a single clustering estimate c based on an MCMC sample of clusterings c(1) , c(2) . . . , c(M ) from the posterior distribution of a Bayesian cluster model. Methods to derive c when the number of groups K varies between the clusterings are reviewed and discussed. These include the maximum a posteriori (MAP) estimate and methods based on the posterior similarity matrix, a matrix containing the posterior probabilities that the observations i and j are in the same cluster. The posterior similarity matrix is related to a commonly used loss function by Binder (1978). Minimization of the loss is shown to be equivalent to maximizing the Rand index between esti- mated and true clustering. We propose new criteria for estimating a clustering, which are based on the posterior expected adjusted Rand index. The criteria are shown to possess a shrinkage property and outperform Binder's loss in a simulation study and in an application to gene expression data. They also perform favorably compared to other clustering procedures.}, author = {Arno Fritsch And Katja Ickstadt}, citeulike-article-id = {5387265}, citeulike-linkout-0 = {http://ba.stat.cmu.edu/vol04is02.php}, journal = {Bayesian analysis}, keywords = {clustering, dirichlet, mixture, model, process, summarize}, posted-at = {2009-10-25 12:30:48}, priority = {2}, title = {Improved Criteria for Clustering Based on the Posterior Similarity Matrix}, url = {http://ba.stat.cmu.edu/vol04is02.php} }

TY - JOUR ID - citeulike:5387265 L3 - citeulike-article-id:5387265 N2 - In this paper we address the problem of obtaining a single clustering estimate c based on an MCMC sample of clusterings c(1) , c(2) . . . , c(M ) from the posterior distribution of a Bayesian cluster model. Methods to derive c when the number of groups K varies between the clusterings are reviewed and discussed. These include the maximum a posteriori (MAP) estimate and methods based on the posterior similarity matrix, a matrix containing the posterior probabilities that the observations i and j are in the same cluster. The posterior similarity matrix is related to a commonly used loss function by Binder (1978). Minimization of the loss is shown to be equivalent to maximizing the Rand index between esti- mated and true clustering. We propose new criteria for estimating a clustering, which are based on the posterior expected adjusted Rand index. The criteria are shown to possess a shrinkage property and outperform Binder’s loss in a simulation study and in an application to gene expression data. They also perform favorably compared to other clustering procedures. JF - Bayesian analysis TI - Improved Criteria for Clustering Based on the Posterior Similarity Matrix KW - clustering KW - dirichlet KW - mixture KW - model KW - process KW - summarize AU - Arno Fritsch And Katja Ickstadt UR - http://ba.stat.cmu.edu/vol04is02.php ER -