  Bayesian hierarchical clustering (BHC) is an agglomerative clustering method,
where a probabilistic model is defined and its marginal likelihoods are
evaluated to decide which clusters to merge. While BHC provides a few
advantages over traditional distance-based agglomerative clustering algorithms,
successive evaluation of marginal likelihoods and careful hyperparameter tuning
are cumbersome and limit the scalability. In this paper we relax BHC into a
non-probabilistic formulation, exploring small-variance asymptotics in
conjugate-exponential models. We develop a novel clustering algorithm, referred
to as relaxed BHC (RBHC), from the asymptotic limit of the BHC model that
exhibits the scalability of distance-based agglomerative clustering algorithms
as well as the flexibility of Bayesian nonparametric models. We also
investigate the reducibility of the dissimilarity measure emerged from the
asymptotic limit of the BHC model, allowing us to use scalable algorithms such
as the nearest neighbor chain algorithm. Numerical experiments on both
synthetic and real-world datasets demonstrate the validity and high performance
of our method.
