  Model-based clustering is widely-used in a variety of application areas.
However, fundamental concerns remain about robustness. In particular, results
can be sensitive to the choice of kernel representing the within-cluster data
density. Leveraging on properties of pairwise differences between data points,
we propose a class of Bayesian distance clustering methods, which rely on
modeling the likelihood of the pairwise distances in place of the original
data. Although some information in the data is discarded, we gain substantial
robustness to modeling assumptions. The proposed approach represents an
appealing middle ground between distance- and model-based clustering, drawing
advantages from each of these canonical approaches. We illustrate dramatic
gains in the ability to infer clusters that are not well represented by the
usual choices of kernel. A simulation study is included to assess performance
relative to competitors, and we apply the approach to clustering of brain
genome expression data.
  Keywords: Distance-based clustering; Mixture model; Model-based clustering;
Model misspecification; Pairwise distance matrix; Partial likelihood;
Robustness.
