An MBO scheme for clustering and semi-supervised clustering of signed networks
This addresses the challenge of partitioning graphs with signed edges for applications like financial analysis, though it appears incremental as it adapts existing numerical schemes to this specific problem.
The authors tackled the problem of clustering signed networks, where edges have positive or negative weights, by developing a method based on the Ginzburg-Landau functional and the Merriman-Bence-Osher scheme, achieving promising results that compare favorably against state-of-the-art approaches on synthetic and real-world datasets.
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.