Unsupervised Clustering on Signed Graphs with Unknown Number of Clusters

We consider the problem of unsupervised clustering on signed graphs, i.e., graphs with positive and negative edge weights. Motivated by signed cut minimization, we propose an optimization problem that minimizes the total variation of the cluster labels subject to constraints on the cluster size, augmented with a regularization that prevents clusters consisting of isolated nodes. We estimate the unknown number of clusters by tracking the change of total variation with successively increasing putative cluster numbers. Simulation results indicate that our method yields excellent results for moderately unbalanced graphs.