maxpear {mcclust}

Maximize/Compute Posterior Expected Adjusted Rand Index

Description

Based on a posterior similarity matrix of a sample of clusterings maxpear finds the clustering that maximizes the posterior expected Rand adjusted index (PEAR) with the true clustering, while pear computes PEAR for several provided clusterings.

Usage

maxpear(psm, cls.draw = NULL, method = c("avg", "comp", "draws",
         "all"), max.k = NULL)

pear(cls,psm)

Arguments

psm

a posterior similarity matrix, usually obtained from a call to comp.psm.

cls, cls.draw

a matrix in which every row corresponds to a clustering of the ncol(cls) objects. cls.draw refers to the clusterings that have been used to compute psm, cls.draw has to be provided if method="draw" or "all".

method

the maximization method used. Should be one of "avg", "comp", "draws" or "all". The default is "avg".

max.k

integer, if method="avg" or "comp" the maximum number of clusters up to which the hierarchical clustering is cut. Defaults to ceiling(nrow(psm)/8).

Details

For method="avg" and "comp" 1-psm is used as a distance matrix for hierarchical clustering with average/complete linkage. The hierachical clustering is cut for the cluster sizes 1:max.k and PEAR computed for these clusterings.
Method "draws" simply computes PEAR for each row of cls.draw and takes the maximum.
If method="all" all maximization methods are applied.

Value

cl

clustering with maximal value of PEAR. If method="all" a matrix containing the clustering with the higest value of PEAR over all methods in the first row and the clusterings of the individual methods in the next rows.

value

value of PEAR. A vector corresponding to the rows of cl if method="all".

method

the maximization method used.

Author(s)

Arno Fritsch, [e-mail]

References

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

See Also

comp.psm for computing posterior similarity matrix, minbinder, medv, relabel for other possibilities for processing a sample of clusterings.

Examples

data(cls.draw1.5) 
# sample of 500 clusterings from a Bayesian cluster model 
tru.class <- rep(1:8,each=50) 
# the true grouping of the observations
psm1.5 <- comp.psm(cls.draw1.5)
mpear1.5 <- maxpear(psm1.5)
table(mpear1.5$cl, tru.class)

# Does hierachical clustering with Ward's method lead 
# to a better value of PEAR?
hclust.ward <- hclust(as.dist(1-psm1.5), method="ward")
cls.ward <- t(apply(matrix(1:20),1, function(k) cutree(hclust.ward,k=k)))
ward1.5 <- pear(cls.ward, psm1.5)
max(ward1.5) > mpear1.5$value