A generalized Bayes framework for probabilistic clustering

Summary Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification uncertainty estimated clusters is a disadvantage. Model-based based on mixture models provides an alternative approach, but methods face computational problems highly sensitive to choice kernel. In this article we propose generalized Bayes framework that bridges between these paradigms through use Gibbs posteriors. conducting Bayesian updating, loglikelihood replaced by loss function clustering, leading rich family methods. The posterior represents coherent updating beliefs without needing specify likelihood data, can be used characterizing clustering. We consider losses Bregman divergence pairwise similarities, develop efficient deterministic algorithms point estimation along with sampling quantification. Several existing algorithms, including k-means, interpreted estimators our framework, thus provide method approaches, allowing, example, calculation probability data well clustered.