N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification (1802.08888v1)

Abstract: Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model improves state-of-the-art baselines on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations.

• The paper introduces a multi-scale N-GCN architecture that fuses outputs from multiple GCN instances based on varying random walk distances to enhance node classification.
• It expands the receptive field by integrating graph convolutions over diverse neighborhood depths, achieving superior accuracy compared to traditional models.
• The model's adaptable design generalizes to other architectures such as GraphSAGE, offering broad applicability in social network, recommendation, and biological network analysis.

Analyzing the Efficacy of Multi-scale Graph Convolution with N-GCN for Semi-supervised Node Classification

The paper "N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification" introduces a novel approach to enhancing semi-supervised learning capabilities on graph-structured data. The authors propose a network architecture, termed as N-GCN, which integrates multiple instances of Graph Convolutional Networks (GCNs) operating on various scales defined by random walk distances. This design promises improvements over existing state-of-the-art models in node classification tasks by capturing information from nodes at varying distances within the graph structure.

Methodological Overview

The core innovation of N-GCN lies in leveraging the representational power of both graph convolutions and random walk statistics. Traditional GCNs, as demonstrated by Kipf and Welling, apply convolutional operations directly on the normalized adjacency matrix to diffuse information through graph edges. However, the proposed model enhances this by generating multiple GCN instances, each focused on node pairs determined by distinct distances in random walks. Thus, it effectively broadens the receptive field across the graph, addressing multiple graph scales simultaneously.

N-GCN comprises several key features:

• Multi-scale Approach: By training GCNs on powers of the normalized adjacency matrix, N-GCN integrates insights spanning various neighborhood depths within a graph.
• Combination of Outputs: A classification sub-network combines outputs from the GCN instances, learning an optimal fusion of multi-scale information to satisfy the classification objective.
• Generalization to Novel Architectures: The versatility of the N-GCN framework allows adaptation to other semi-supervised models such as GraphSAGE, introducing variations like N-SAGE.

Experimentation and Results

Extensive experiments highlight N-GCN’s robustness and efficacy. The model demonstrates significant improvements over typical GCN and GraphSAGE baselines, achieving superior node classification accuracy on datasets like Cora, Citeseer, Pubmed, and PPI. The model’s ability to generalize across different tasks and datasets, showcasing resilience to adversarial input perturbations, is particularly noteworthy. The performance gains underscore the importance of integrating diverse graph scales in enhancing the learning process.

Furthermore, sensitivity analyses reveal the impact of the number of random walk steps (K) and the replication factor (r) on performance. Notably, the results suggest that introducing multiple scales of adjacency (via random walks) yields more improvement than simply increasing model capacity.

Theoretical and Practical Implications

The work sets a precedent for the effective exploitation of multiple scales in graph convolutional setups. By accruing signals from both immediate and distant nodes, the theoretical underpinning suggests a pathway for better capturing the relational and structural complexity inherent in graph-based data. Practically, such advancements are alignable with applications in social network analysis, recommendation systems, and biological networks, where node classification plays a pivotal role.

Future Trajectories

The paper opens avenues for further exploration into adaptive graph methods. Envisioning stochastic implementations could drive N-GCN’s application to larger graphs, enhancing scalability. Additionally, extending the methodology to unsupervised settings or other domain-specific graph models could further push the boundaries of graph convolutional networks. Integrating self-supervised learning paradigms might also complement and expand on the semi-supervised achievements presented.

In summary, the introduction of N-GCN reflects a strategic evolution in leveraging multi-scale node relationships and graph convolutional structures, offering a structured path forward in graph-based machine learning tasks.