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We introduce a principled method for the signed clustering problem, where thegoal is to partition a graph whose edge weights take both positive and negativevalues, such that edges within the same cluster are mostly positive, whileedges spanning across clusters are mostly negative. Our method relies on agraph-based diffuse interface model formulation utilizing the Ginzburg-Landaufunctional, based on an adaptation of the classic numericalMerriman-Bence-Osher (MBO) scheme for minimizing such graph-based functionals.The proposed objective function aims to minimize the total weight ofinter-cluster positively-weighted edges, while maximizing the total weight ofthe inter-cluster negatively-weighted edges. Our method scales to large sparsenetworks, and can be easily adjusted to incorporate labelled data information,as is often the case in the context of semi-supervised learning. We tested ourmethod on a number of both synthetic stochastic block models and real-worlddata sets (including financial correlation matrices), and obtained promisingresults that compare favourably against a number of state-of-the-art approachesfrom the recent literature.

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