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

arXiv: https://arxiv.org/abs/1901.03091 · HTML: https://mlsanity.com/paper/1901.03091/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2019.

## Built on by (most cited first, 2 of 2)

- [SSSNET: Semi-Supervised Signed Network Clustering](https://mlsanity.com/paper/2110.06623/) (2021)
- [Gradient flows and randomised thresholding: sparse inversion and classification](https://mlsanity.com/paper/2203.11555/) (2022)

## Abstract (arXiv)

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.