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