Balanced clustering is an important topic in unsupervised learning. In essence, many real-world applications require the obtained clusters to be balanced. However, the balanced property of previous graph-based models rely on specific assumptions of the input data so there is no guarantee to obtain balanced clusters. On the contrary, our proposed Exp-Cut can provide not only a balanced tendency but also rigorously balanced clusters with strong theoretical guarantees via hyperparameter turning. In addition, we propose a novel and efficient heuristic solver that can solve not only the proposed Exp-Cut model but also any other graph-cut models. Developing new graph models will be much easier with the help of our solver.

Recently, balanced graph-based clustering has been a hot issue in clustering domain, but the balanced theoretical guarantees of previous models are either qualitative or based on a probabilistic random graph, which may fail to various real data. To make up this vital flaw, this letter explores a novel balanced graph-based clustering model, named exponential-cut (Exp-Cut), via redesigning the intercluster compactness based on the exponential transformation $\exp \lbrace \mu x\rbrace$. It is worth noting that exponential transformation not only provides a bounded balanced tendency for Exp-Cut, but also helps Exp-Cut to achieve balanced results on an arbitrary graph via adjusting its curvature $\mu$. To solve the optimization problem involved in Exp-Cut model, an efficient heuristic solver is proposed and the computational complexity is $\mathcal {O}(n^2)$ per iteration. Experimental results demonstrate that our proposals outperform competitors on all benchmarks with respect to clustering performance, balanced property, and efficiency.