Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Deep Signed Graph Clustering via Weak Balance Theory

Peiyao Zhao, Xin Li, Zeyu Zhang, Mingzhong Wang, Xueying Zhu, Lejian Liao

TL;DR

This work tackles robustness in signed graph clustering by moving beyond traditional Balance Theory to Weak Balance Theory, enabling effective K-way clustering in the presence of noise. It introduces DSGC, a framework comprising Violation Sign-Refine and Density-based Augmentation for graph rewiring, a clustering-oriented signed encoder, and a differentiable K-way clustering loss that minimizes intra-cluster positives and inter-cluster negatives. Empirical results on synthetic and real-world datasets show DSGC achieves state-of-the-art performance across multiple metrics and settings, with ablations confirming the contribution of each component and the importance of handling negative edges for clear cluster delineation. The approach offers a scalable, unsupervised pathway to robustly uncover multi-cluster structure in complex signed networks, with demonstrated benefits in downstream tasks like link prediction on unlabeled graphs.

Abstract

Signed graph clustering is a critical technique for discovering community structures in graphs that exhibit both positive and negative relationships. We have identified two significant challenges in this domain: i) existing signed spectral methods are highly vulnerable to noise, which is prevalent in real-world scenarios; ii) the guiding principle ``an enemy of my enemy is my friend'', rooted in \textit{Social Balance Theory}, often narrows or disrupts cluster boundaries in mainstream signed graph neural networks. Addressing these challenges, we propose the \underline{D}eep \underline{S}igned \underline{G}raph \underline{C}lustering framework (DSGC), which leverages \textit{Weak Balance Theory} to enhance preprocessing and encoding for robust representation learning. First, DSGC introduces Violation Sign-Refine to denoise the signed network by correcting noisy edges with high-order neighbor information. Subsequently, Density-based Augmentation enhances semantic structures by adding positive edges within clusters and negative edges across clusters, following \textit{Weak Balance} principles. The framework then utilizes \textit{Weak Balance} principles to develop clustering-oriented signed neural networks to broaden cluster boundaries by emphasizing distinctions between negatively linked nodes. Finally, DSGC optimizes clustering assignments by minimizing a regularized clustering loss. Comprehensive experiments on synthetic and real-world datasets demonstrate DSGC consistently outperforms all baselines, establishing a new benchmark in signed graph clustering.

Robust Deep Signed Graph Clustering via Weak Balance Theory

TL;DR

This work tackles robustness in signed graph clustering by moving beyond traditional Balance Theory to Weak Balance Theory, enabling effective K-way clustering in the presence of noise. It introduces DSGC, a framework comprising Violation Sign-Refine and Density-based Augmentation for graph rewiring, a clustering-oriented signed encoder, and a differentiable K-way clustering loss that minimizes intra-cluster positives and inter-cluster negatives. Empirical results on synthetic and real-world datasets show DSGC achieves state-of-the-art performance across multiple metrics and settings, with ablations confirming the contribution of each component and the importance of handling negative edges for clear cluster delineation. The approach offers a scalable, unsupervised pathway to robustly uncover multi-cluster structure in complex signed networks, with demonstrated benefits in downstream tasks like link prediction on unlabeled graphs.

Abstract

Signed graph clustering is a critical technique for discovering community structures in graphs that exhibit both positive and negative relationships. We have identified two significant challenges in this domain: i) existing signed spectral methods are highly vulnerable to noise, which is prevalent in real-world scenarios; ii) the guiding principle ``an enemy of my enemy is my friend'', rooted in \textit{Social Balance Theory}, often narrows or disrupts cluster boundaries in mainstream signed graph neural networks. Addressing these challenges, we propose the \underline{D}eep \underline{S}igned \underline{G}raph \underline{C}lustering framework (DSGC), which leverages \textit{Weak Balance Theory} to enhance preprocessing and encoding for robust representation learning. First, DSGC introduces Violation Sign-Refine to denoise the signed network by correcting noisy edges with high-order neighbor information. Subsequently, Density-based Augmentation enhances semantic structures by adding positive edges within clusters and negative edges across clusters, following \textit{Weak Balance} principles. The framework then utilizes \textit{Weak Balance} principles to develop clustering-oriented signed neural networks to broaden cluster boundaries by emphasizing distinctions between negatively linked nodes. Finally, DSGC optimizes clustering assignments by minimizing a regularized clustering loss. Comprehensive experiments on synthetic and real-world datasets demonstrate DSGC consistently outperforms all baselines, establishing a new benchmark in signed graph clustering.

Paper Structure

This paper contains 31 sections, 3 theorems, 13 equations, 14 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Notations
  5. Relaxation of Social Balance
  6. Problem Definition
  7. Methodology
  8. Signed Graph Rewiring
  9. Violation Sign-Refine
  10. Density-based Augmentation
  11. Signed Clustering Encoder
  12. $K$-way Signed Graph Clustering
  13. Experiments
  14. Experimental Settings
  15. Datasets.
  16. ...and 16 more sections

Key Result

Lemma 1

For $v_i$, $v_j\in \mathcal{V}$ in a signed graph $\mathcal{G}=\{\mathcal{V},\mathcal{E}, \mathbf{X}\}$, let $\mu_l^{+}(i,j)$ and $\mu_l^{-}(i,j)$ be the number of positive and negative walks with length $l$ connecting $v_i$ and $v_j$, respectively. Then, $\forall a\in \mathbb{N}$,

Figures (14)

  • Figure 1: Effects of different perturbations, including flipping signs and randomly adding negative edges, on the clustering performance of popular spectral methods in signed graphs.
  • Figure 2: Illustration of "an Enemy of my Enemy is my Friend (EEF)" narrowing cluster boundaries. Aggregating positive (/ negative) neighbors $1\& 2$ (/ $3 \& 4$) causes $\mathbf{Z}^{+}_{i}$ (/ $\mathbf{Z}^{-}_{i}$) mapped far from its clusters or even cross the boundary, where positive (/ negative) neighbors $2$ (/ $3$) are defined by "EEF".
  • Figure 3: The overall framework of DSGC. The Violation Sign-Refine first computes non-noise scores to correct the signs of noisy edges. Then, the Density-based Augmentation adds positive edges within clusters and negative edges across clusters. These two rewiring methods generate a new adjacency matrix with reduced noise and enhanced semantic structures. Thereafter, clustering-specific signed convolutional networks can be trained by minimizing the differential clustering loss for learning and strengthening the discrimination among node representations linked negatively.
  • Figure 4: Ablation study. (a)$\sim$(d) ACC($\%$) vs. edge probability $p$, flip probability $\eta$, node number $N$ and cluster number $K$.
  • Figure 5: The impact of the term $(-\bar{\mathbf{A}}^{-})$ and "EEF" principle on ACC (%) (Top) and SoEN (Bottom).
  • ...and 9 more figures

Theorems & Definitions (4)

  • Definition 1
  • Lemma 1
  • Theorem 1: Social Balance Theory
  • Theorem 2: Weak Balance Theory