relabel: 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.
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.
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.
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.
# NOT RUN {(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
# }