An MBO scheme for clustering and semi-supervised clustering of signed networks

We introduce a principled method for the signed clustering problem, where goal is to partition weighted undirected graph whose edge weights take both positive and negative values, such that edges within same cluster are mostly positive, while spanning across clusters negative. Our relies on graph-based diffuse interface model formulation utilizing Ginzburg-Landau functional, based an adaptation of classic numerical Merriman-Bence-Osher (MBO) scheme minimizing functionals. The proposed object ive function aims minimize total weight inter-cluster positively-weighted edges, maximizing negatively-weighted edges. scales large sparse networks, can be easily adjusted incorporate labelled data information, as often case in context semisupervised learning. tested our number synthetic stochastic block models real-world sets (including financial correlation matrices), obtained promising results compare favourably against state-of-the-art approaches from recent literature.