  Cluster analysis is a popular unsupervised learning tool used in many
disciplines to identify heterogeneous sub-populations within a sample. However,
validating cluster analysis results and determining the number of clusters in a
data set remains an outstanding problem. In this work, we present a global
criterion called the Distinguishability criterion to quantify the separability
of identified clusters and validate inferred cluster configurations. Our
computational implementation of the Distinguishability criterion corresponds to
the Bayes risk of a randomized classifier under the 0-1 loss. We propose a
combined loss function-based computational framework that integrates the
Distinguishability criterion with many commonly used clustering procedures,
such as hierarchical clustering, k-means, and finite mixture models. We present
these new algorithms as well as the results from comprehensive data analysis
based on simulation studies and real data applications.
