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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper introduces max-margin Bayesian clustering (BMC) that extends Bayesian clustering techniques to include the max-margin criterion. This includes, for example, the Dirichlet process max-margin Gaussian mixture that relaxes the underlying Gaussian assumption of Dirichlet process Gaussian mixtures by incorporating max-margin posterior constraints, and is able to infer the number of clusters from data. The resulting techniques (DPMMGM and a further one classed MMCTM) are compared to a variety of other techniques in several numerical experiments. The paper combines two clustering approaches: Deterministic and Bayesian clustering.