Abstract

Estimating the number of clusters remains a difficult model selection problem. We consider this problem in the domain where the affinity relations involve groups of more than two nodes. Building on the previous formulation for the pairwise affinity case, we exploit the mathematical structures in the higher order case. We express the original minimal-rank and positive semi-definite (PSD) constraints in a form amenable for numerical implementation, as the original constraints are either intractable or even undefined in general in the higher order case. To scale to large problem sizes, we also propose an alternative formulation, so that it can be efficiently solved via stochastic optimization in an online fashion. We evaluate our algorithm with different applications to demonstrate its superiority, and show itcan adapt to varying levels of unbalancedness of clusters.