[Paper Review] Signed Graph Convolutional Network

Tyler Derr, Yao Ma+1 more|arXiv (Cornell University)|Aug 20, 2018

Advanced Graph Neural NetworksComputer Science27 references56 citations

TL;DR

Introduces Signed Graph Convolutional Network (SGCN) that uses balance theory to integrate positive and negative links in signed networks, enabling effective node embeddings and link sign prediction. It aggregates information via balanced and unbalanced paths across multiple layers and optimizes with a balance-theory based loss.

ABSTRACT

Due to the fact much of today's data can be represented as graphs, there has been a demand for generalizing neural network models for graph data. One recent direction that has shown fruitful results, and therefore growing interest, is the usage of graph convolutional neural networks (GCNs). They have been shown to provide a significant improvement on a wide range of tasks in network analysis, one of which being node representation learning. The task of learning low-dimensional node representations has shown to increase performance on a plethora of other tasks from link prediction and node classification, to community detection and visualization. Simultaneously, signed networks (or graphs having both positive and negative links) have become ubiquitous with the growing popularity of social media. However, since previous GCN models have primarily focused on unsigned networks (or graphs consisting of only positive links), it is unclear how they could be applied to signed networks due to the challenges presented by negative links. The primary challenges are based on negative links having not only a different semantic meaning as compared to positive links, but their principles are inherently different and they form complex relations with positive links. Therefore we propose a dedicated and principled effort that utilizes balance theory to correctly aggregate and propagate the information across layers of a signed GCN model. We perform empirical experiments comparing our proposed signed GCN against state-of-the-art baselines for learning node representations in signed networks. More specifically, our experiments are performed on four real-world datasets for the classical link sign prediction problem that is commonly used as the benchmark for signed network embeddings algorithms.

Motivation & Objective

• Motivate learning node representations in signed networks where links can be positive or negative.
• Propose a principled GCN variant that respects balance theory to aggregate both positive and negative information.
• Develop an objective function that guides embedding learning for signed relationships.
• Demonstrate effectiveness on real-world signed networks for link sign prediction.

Proposed method

• Extend unsigned GCNs to signed networks by introducing balanced and unbalanced path-based aggregations.
• Define B(l) and U(l) sets to capture balanced and unbalanced paths up to layer l using balance theory.
• Maintain two representations per node at each layer: a 'friends' (balanced) and an 'enemies' (unbalanced) representation.
• Use layer-wise aggregators with weight matrices W^(l) to propagate information from N_i^+(positive) and N_i^-(negative) accordingly.
• Propose Algorithm 2 to generate final embeddings by concatenating h_i^{B(L)} and h_i^{U(L)} for each node.
• Form an objective with a supervised multinomial logistic regression component for link type classification and a second term based on extended structural balance theory, optimized via SGD with regularization.

Experimental results

Research questions

• RQ1 Can SGCN learn meaningful low-dimensional embeddings for nodes in signed networks?
• RQ2 Does incorporating balance theory and longer aggregation paths improve signed network embeddings compared to baselines?
• RQ3 How do balanced and unbalanced path aggregations contribute to predictive performance on link signs?
• RQ4 What is the impact of using only first-layer aggregation versus multi-layer balance-theory informed aggregation?

Key findings

• SGCN demonstrates improved performance for link sign prediction over state-of-the-art baselines on four real-world signed networks.
• Incorporating balance theory and longer path information enhances embedding quality beyond single-layer aggregation.
• The model learns dual representations per node (friends and enemies) that effectively propagate via balanced/unbalanced paths across layers.
• The objective combines a supervised classifier term with a balance-theory based ranking term to structure the embedding space.