relabel {mcclust}

Stephens' Relabelling Algorithm for Clusterings

Description

For a sample of clusterings in which corresponding clusters have different labels the algorithm attempts to bring the clusterings to a unique labelling.

Usage

relabel(cls, print.loss = TRUE)

Arguments

cls

a matrix in which every row corresponds to a clustering of the ncol(cls) objects.

print.loss

logical, should current value of loss function be printed after each iteration? Defaults to TRUE.

Details

The algorithm minimizes the loss function

\sum_{m=1}^M\sum_{i=1}^n\sum_{j=1}^K-\log\hat{p}_{ij} \cdot I_{\{z_i^{(m)}=j\}}

over the M clusterings, n observations and K clusters, where \hat{p}_{ij} is the estimated probability that observation i belongs to cluster j and z_i^{(m)} indicates to which cluster observation i belongs in clustering m. I_{\{.\}} is an indicator function.

Minimization is achieved by iterating the estimation of \hat{p}_{ij} over all clusterings and the minimization of the loss function in each clustering by permuting the cluster labels. The latter is done by linear programming.

Value

cls

the input cls with unified labelling.

P

an n \times K matrix, where entry [i,j] contains the estimated probability that observation i belongs to cluster j.

loss.val

value of the loss function.

cl

vector of cluster memberships that have the highest probabilities \hat{p}_{ij}.

Warning

The algorithm assumes that the number of clusters K is fixed. If this is not the case K is taken to be the most common number of clusters. Clusterings with other numbers of clusters are discarded and a warning is issued.

Note

The implementation is a variant of the algorithm of Stephens which is originally applied to draws of parameters for each observation, not to cluster labels.

Author(s)

Arno Fritsch, [e-mail]

References

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

See Also

lp.transport for the linear programming, maxpear, minbinder, medv for other possibilities of processing a sample of clusterings.

Examples

(cls <- rbind(c(1,1,2,2),c(1,1,2,2),c(1,2,2,2),c(2,2,1,1)))
# group 2 in clustering 4 corresponds to group 1 in clustering 1-3.
cls.relab <- relabel(cls)
cls.relab$cls