Abstract

While clustering has been well studied in the past decade, model selection has drawn less attention. This paper addresses both problems in a joint manner with an indicator matrix formulation, in which the clustering cost is penalized by a Frobenius inner product term and the group number estimation is achieved by a rank minimization. As affifinity graphs generally contain positive edge values, a sparsity term is further added to avoid the trivial solution. Rather than adopting the conventional convex relaxation approach wholesale, we represent the original problem more faithfully by taking full advantage of the particular structure present in the optimization problem and solving it effificiently using the Alternating Direction Method of Multipliers. The highly constrained nature of the optimization provides our algorithm with the robustness to deal with the varying and often imperfect input affifinity matrices arising from different applications and different group numbers. Evaluations on the synthetic data as well as two real world problems show the superiority of the method across a large variety of settings.