[Paper Review] SSSNET: Semi-Supervised Signed Network Clustering

Yixuan He, Gesine Reinert+2 more|arXiv (Cornell University)|Oct 13, 2021

Complex Network Analysis Techniques4 citations

TL;DR

SSSNET is a novel graph neural network framework for semi-supervised signed network clustering that introduces a probabilistic balanced normalized cut loss and a Signed Mixed-Path Aggregation (SIMPA) scheme, enabling end-to-end learning without intermediate steps. It outperforms state-of-the-art methods on synthetic and real-world datasets, especially under high noise and sparsity, by adopting a neutral stance on social balance theory, avoiding the assumption that 'an enemy's enemy is a friend'.

ABSTRACT

Node embeddings are a powerful tool in the analysis of networks; yet, their full potential for the important task of node clustering has not been fully exploited. In particular, most state-of-the-art methods generating node embeddings of signed networks focus on link sign prediction, and those that pertain to node clustering are usually not graph neural network (GNN) methods. Here, we introduce a novel probabilistic balanced normalized cut loss for training nodes in a GNN framework for semi-supervised signed network clustering, called SSSNET. The method is end-to-end in combining embedding generation and clustering without an intermediate step; it has node clustering as main focus, with an emphasis on polarization effects arising in networks. The main novelty of our approach is a new take on the role of social balance theory for signed network embeddings. The standard heuristic for justifying the criteria for the embeddings hinges on the assumption that "an enemy's enemy is a friend". Here, instead, a neutral stance is assumed on whether or not the enemy of an enemy is a friend. Experimental results on various data sets, including a synthetic signed stochastic block model, a polarized version of it, and real-world data at different scales, demonstrate that SSSNET can achieve comparable or better results than state-of-the-art spectral clustering methods, for a wide range of noise and sparsity levels. SSSNET complements existing methods through the possibility of including exogenous information, in the form of node-level features or labels.

Motivation & Objective

• To address the gap in graph neural network-based methods for signed network clustering, particularly those that integrate node clustering as the primary objective.
• To overcome the limitations of existing methods that rely on strong assumptions of social balance theory, such as 'an enemy’s enemy is a friend'.
• To develop an end-to-end framework that unifies node embedding generation and clustering, enabling the use of exogenous node features or labels.
• To improve clustering performance under varying noise and sparsity levels, especially in polarized and sparse network settings.
• To provide a self-supervised training objective that generalizes beyond strict social balance, enhancing robustness on real-world networks with inconsistent triadic structures.

Proposed method

• Proposes a new probabilistic balanced normalized cut (PBNC) loss as a self-supervised objective to guide clustering in signed networks, promoting balanced and normalized cluster assignments.
• Introduces Signed Mixed-Path Aggregation (SIMPA), a novel message-passing mechanism that decouples positive and negative edge propagation, allowing flexible modeling of friend and foe relationships.
• Employs four separate multi-layer perceptrons (MLPs) to process node features and propagate embeddings through positive and negative edges separately, enabling distinct learning for different relationship types.
• Combines a self-supervised PBNC loss with a supervised loss on labeled seed nodes, enabling semi-supervised training and improved generalization.
• Uses a final linear layer with softmax to produce cluster probability distributions, with argmax used to assign final cluster labels.
• Adopts a neutral stance on social balance theory by not enforcing that 'an enemy’s enemy is a friend', instead allowing the model to learn from data whether such relationships emerge.

Experimental results

Research questions

• RQ1 Can a GNN-based method achieve state-of-the-art performance in signed network clustering without relying on strict social balance assumptions?
• RQ2 How does the proposed probabilistic balanced normalized cut loss compare to traditional spectral clustering methods under varying levels of noise and sparsity?
• RQ3 To what extent does the SIMPA aggregation mechanism improve clustering performance compared to standard GNNs or those enforcing social balance?
• RQ4 How effective is SSSNET in handling real-world signed networks with ground-truth labels, especially in polarized or sparse regimes?
• RQ5 Can the integration of exogenous node features or labels significantly improve clustering accuracy in semi-supervised settings?

Key findings

• SSSNET achieves the highest Adjusted Rand Index (ARI) on the S&P 1500 and Sampson datasets, outperforming all baselines in both fully and semi-supervised settings.
• On the Fin-YNet dataset, SSSNET achieves the most consistent performance across 21 years, with the lowest average distance to the best-performing method (ARI dist. to best: 0.00 ± 0.00).
• In self-supervised settings without labels, SSSNET achieves a lower 'unhappy ratio' (ratio of edges violating cluster assignments) than competing methods, indicating better clustering quality.
• Ablation studies confirm that removing the PBNC loss increases the unhappy ratio, demonstrating its critical role in performance.
• When compared to a variant enforcing social balance theory, SSSNET shows higher ARI, especially as violation ratios increase, validating the benefit of its neutral stance.
• Increasing the seed node ratio improves test ARI, confirming the effectiveness of semi-supervised supervision in the framework.