Process MCMC Sample of Clusterings.

Description

Implements methods for processing a sample of (hard) clusterings, e.g. the MCMC output of a Bayesian clustering model. Among them are methods that find a single best clustering to represent the sample, which are based on the posterior similarity matrix or a relabelling algorithm.

Details

Most important functions:

comp.psm for computing posterior similarity matrix (PSM). Based on the PSM maxpear and minbinder provide several optimization methods to find a clustering with maximal posterior expected adjusted Rand index with the true clustering or one that minimizes the posterior expectation of a loss function by Binder (1978). minbinder provides the optimization algorithm of Lau and Green.

relabel contains the relabelling algorithm of Stephens (2000).

arandi and vi.dist compute distance functions for clusterings, the (adjusted) Rand index and the entropy-based variation of information distance.

Author(s)

Arno Fritsch

Maintainer: Arno Fritsch <arno.fritsch@tu-dortmund.de>

References

Binder, D.A. (1978) Bayesian cluster analysis, Biometrika 65, 31–38.

Fritsch, A. and Ickstadt, K. (2009) An improved criterion for clustering based on the posterior similarity matrix, Bayesian Analysis, accepted.

Lau, J.W. and Green, P.J. (2007) Bayesian model based clustering procedures, Journal of Computational and Graphical Statistics 16, 526–558.

Stephens, M. (2000) Dealing with label switching in mixture models. Journal of the Royal Statistical Society Series B, 62, 795–809.

Examples

data(cls.draw2) 
# sample of 500 clusterings from a Bayesian cluster model 
tru.class <- rep(1:8,each=50) 
# the true grouping of the observations
psm2 <- comp.psm(cls.draw2)
# posterior similarity matrix

# optimize criteria based on PSM
mbind2 <- minbinder(psm2)
mpear2 <- maxpear(psm2)

# Relabelling  
k <- apply(cls.draw2,1, function(cl) length(table(cl)))
max.k <- as.numeric(names(table(k))[which.max(table(k))])
relab2 <- relabel(cls.draw2[k==max.k,])

# compare clusterings found by different methods with true grouping
arandi(mpear2$cl, tru.class)
arandi(mbind2$cl, tru.class)
arandi(relab2$cl, tru.class)

Results