Model-based clustering with soft balancing

Balanced clustering algorithms can be useful in a variety of applications and have recently attracted increasing research interest. Most recent work, however, addressed only hard balancing by constraining each cluster to have equal or a certain minimum number of data objects. We provide a soft balancing strategy built upon a soft mixture-of-models clustering framework. This strategy constrains the sum of posterior probabilities of object membership for each cluster to be equal and thus balances the expected number of data objects in each cluster. We first derive soft model-based clustering from an information-theoretic viewpoint and then show that the proposed balanced clustering can be parameterized by a temperature parameter that controls the softness of clustering as well as that of balancing. As the temperature decreases, the resulting partitioning becomes more and more balanced. In the limit, when temperature becomes zero, the balancing becomes hard and the actual partitioning becomes perfectly balanced. The effectiveness of the proposed soft balanced clustering algorithm is demonstrated on both synthetic and real text data.