We introduce a principled method for the signed clustering problem, where the goal is to partition a weighted undirected 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 semisupervised 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.

中文翻译：

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用于签名网络的集群和半监督集群的MBO方案

我们针对有符号聚类问题介绍了一种有原则的方法，其目标是对加权无向图进行划分，该图的边缘权重同时为正值和负值，从而使同一聚类中的边缘大部分为正，而跨聚类的边缘大部分为负。 。我们的方法依赖于利用基于Ginzburg-Landau函数的基于图的扩散接口模型公式，该模型基于经典数值Merriman-Bence-Osher（MBO）方案的改编，以最小化此类基于图的函数。提出的目标函数旨在最大程度地减少群集间正加权边缘的总权重，同时最大程度地增加群集间负加权边缘的总权重。我们的方法可以扩展到大型稀疏网络，并且可以轻松地进行调整以合并标记的数据信息，在半监督学习中通常是这样。我们在大量的合成随机区块模型和现实世界的数据集（包括财务相关矩阵）上测试了我们的方法，并获得了可喜的结果，可与最近文献中的许多最新方法进行比较。