  In this paper we propose a measure of clustering quality or accuracy that is
appropriate in situations where it is desirable to evaluate a clustering
algorithm by somehow comparing the clusters it produces with ``ground truth'
consisting of classes assigned to the patterns by manual means or some other
means in whose veracity there is confidence. Such measures are refered to as
``external'. Our measure also has the characteristic of allowing clusterings
with different numbers of clusters to be compared in a quantitative and
principled way. Our evaluation scheme quantitatively measures how useful the
cluster labels of the patterns are as predictors of their class labels. In
cases where all clusterings to be compared have the same number of clusters,
the measure is equivalent to the mutual information between the cluster labels
and the class labels. In cases where the numbers of clusters are different,
however, it computes the reduction in the number of bits that would be required
to encode (compress) the class labels if both the encoder and decoder have free
acccess to the cluster labels. To achieve this encoding the estimated
conditional probabilities of the class labels given the cluster labels must
also be encoded. These estimated probabilities can be seen as a model for the
class labels and their associated code length as a model cost.
