  Identifying a set of homogeneous clusters in a heterogeneous dataset is one
of the most important classes of problems in statistical modeling. In the realm
of unsupervised partitional clustering, k-means is a very important algorithm
for this. In this technical report, we develop a new k-means variant called
Augmented k-means, which is a hybrid of k-means and logistic regression. During
each iteration, logistic regression is used to predict the current cluster
labels, and the cluster belonging probabilities are used to control the
subsequent re-estimation of cluster means. Observations which can't be firmly
identified into clusters are excluded from the re-estimation step. This can be
valuable when the data exhibit many characteristics of real datasets such as
heterogeneity, non-sphericity, substantial overlap, and high scatter. Augmented
k-means frequently outperforms k-means by more accurately classifying
observations into known clusters and / or converging in fewer iterations. We
demonstrate this on both simulated and real datasets. Our algorithm is
implemented in Python and will be available with this report.
