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AM-GCN: Adaptive Multi-channel Graph Convolutional Networks

Xiao Wang, Meiqi Zhu, Deyu Bo, Peng Cui, Chuan Shi, Jian Pei

arXiv:2007.02265v2cs.LGcs.SIeess.SP

TL;DR

The paper investigates whether GCNs adequately fuse node features and topological structures, finding that their fusion capability is often unsatisfactory. It proposes AM-GCN, which jointly learns specific and common embeddings across feature and topology spaces and adaptively weights them. Extensive benchmark experiments report superior performance over state-of-the-art models and stronger extraction of correlated information from both sources.

  • Problem

    GCNs may inadequately fuse node features and topological structures, even when one source clearly correlates with node labels, raising a fundamental question about what information they learn and combine.

  • Method

    AM-GCN simultaneously learns specific and common embeddings from node features, topology, and their combinations, using feature and topology graphs, shared parameters, and attention-based weighting.

  • Results

    Extensive experiments on benchmark data sets show that AM-GCN outperforms state-of-the-art GCNs and extracts correlated information from both node features and topological structures.

  • Takeaways & Limitations

    AM-GCN provides an adaptive multi-channel framework for fusing feature-space and topology-space information in semi-supervised node classification.

  • Takeaways & Limitations

    The model is studied for semi-supervised node classification on attributed graphs with binary symmetric adjacency matrices and nodes assigned to one of C classes.

Abstract

from arXiv · show

Graph Convolutional Networks (GCNs) have gained great popularity in tackling various analytics tasks on graph and network data. However, some recent studies raise concerns about whether GCNs can optimally integrate node features and topological structures in a complex graph with rich information. In this paper, we first present an experimental investigation. Surprisingly, our experimental results clearly show that the capability of the state-of-the-art GCNs in fusing node features and topological structures is distant from optimal or even satisfactory. The weakness may severely hinder the capability of GCNs in some classification tasks, since GCNs may not be able to adaptively learn some deep correlation information between topological structures and node features. Can we remedy the weakness and design a new type of GCNs that can retain the advantages of the state-of-the-art GCNs and, at the same time, enhance the capability of fusing topological structures and node features substantially? We tackle the challenge and propose an adaptive multi-channel graph convolutional networks for semi-supervised classification (AM-GCN). The central idea is that we extract the specific and common embeddings from node features, topological structures, and their combinations simultaneously, and use the attention mechanism to learn adaptive importance weights of the embeddings. Our extensive experiments on benchmark data sets clearly show that AM-GCN extracts the most correlated information from both node features and topological structures substantially, and improves the classification accuracy with a clear margin.

1 INTRODUCTION

The paper finds that GCNs fuse topology and node features inadequately, motivating AM-GCN, which adaptively combines information from both spaces and their shared embeddings.

  • Background: GCNs are widely used for graph analytics through message passing that aggregates neighboring node features over network topology.The resulting node embeddings support tasks including node and graph classification, link prediction, and recommendation.
  • Motivation: Experiments show GCN fusion of topological structures and node features is distant from optimal, even when either source clearly correlates with labels.The weakness can hinder classification because GCNs may fail to adaptively learn correlations between topology and node features.
  • Motivation: The paper asks whether GCNs can retain their advantages while substantially improving adaptive fusion of topological structures and node features.This question follows the identified weakness in existing GCN fusion mechanisms.
  • AM-GCN: AM-GCN learns node embeddings from node features, topological structures, and their combinations simultaneously for semi-supervised classification.Its design reflects that classification may depend on topology, features, or both.
  • AM-GCN: AM-GCN uses feature-space and topology-space convolution modules, a common convolution module, and attention to adaptively weight the resulting information.The common module captures shared characteristics, while attention learns importance weights for fusion.
  • Results: Extensive benchmark experiments show AM-GCN outperforms state-of-the-art GCNs and extracts correlated information from both node features and topology.The reported gains concern challenging classification tasks across a series of benchmark data sets.

2 FUSION CAPABILITY OF GCNS: AN EXPERIMENTAL INVESTIGATION

Two controlled cases test whether GCNs can adaptively prioritize the label-correlated source of information. In both cases, GCN underperforms a model using the relevant source alone, supporting the paper’s conclusion that its fusion mechanism is inadequate.

  • Experimental design: The experiments construct two simple cases where node labels are highly correlated with either node features or topological structure.The design tests whether GCN can use label supervision to extract the most correlated information.
  • Case 1: Correlated Node Features: In the feature-correlated case, the network topology is random while node features are generated from class-specific Gaussian distributions.The feature vectors have 50 dimensions, and three class distributions share covariance but have distant centers.
  • Case 1: Correlated Node Features: GCN cannot adaptively avoid interference from random topology and therefore fails to match MLP when node features strongly correlate with labels.The authors interpret the performance gap as evidence of inadequate feature-topology fusion.
  • Case 2: Correlated Topology: In the topology-correlated case, node features are random and labels are determined by three communities generated with a stochastic blockmodel.Within-community edges are more probable than between-community edges.
  • Case 2: Correlated Topology: 87% and 100% are the classification accuracies of GCN and DeepWalk, respectively, when topology determines the labels.DeepWalk ignores node features and models the network topology.
  • Summary: Across both cases, GCN cannot fully exploit supervision to extract the most correlated source, showing its current fusion mechanism is distant from satisfactory.The paper notes that real tasks make the choice harder because topology and features may each contribute or jointly matter.

3 AM-GCN: THE PROPOSED MODEL

AM-GCN models semi-supervised node classification by propagating features through both topology and feature spaces, extracting specific and shared embeddings, and adaptively weighting them for prediction.

  • Problem Settings: AM-GCN represents an attributed graph with adjacency matrix A, node-feature matrix X, and C possible node classes.
  • Specific Convolution Module: Specific convolution modules propagate X over feature and topology graphs to learn feature-specific embedding ZF and topology-specific embedding ZT.The topology-space embedding is computed analogously to the feature-space embedding.
  • Specific Convolution Module: A feature-space kNN graph is constructed from node-feature similarities, then used alongside the original topology graph.The method computes similarities among node feature vectors, selects the top k similar node pairs for each node, and forms adjacency matrix Af.
  • Common Convolution Module: A shared-weight Common-GCN extracts common information from the feature and topology spaces, producing shared embeddings ZCF and ZCT and their common embedding ZC.The common embedding is defined as ZC = (ZCT + ZCF)/2.
  • Attention Mechanism: An attention mechanism assigns node-level importance weights to ZT, ZC, and ZF, combining them as Z = αT · ZT + αC · ZC + αF · ZF.Higher attention values indicate greater importance for the corresponding embedding.
  • Objective Function: The objective combines supervised cross-entropy with consistency and disparity constraints, optimized by backpropagation for classification.Consistency aligns similarity matrices from the two Common-GCN outputs, while HSIC-based disparity separates specific and common embeddings.

4 EXPERIMENTS

Experiments evaluate AM-GCN across six datasets, label rates, baselines, variants, embedding visualizations, attention behavior, and parameter settings. AM-GCN generally performs best, while its adaptive fusion, constraints, and attention mechanisms receive supporting evidence.

  • Experimental Setup: AM-GCN is evaluated on six real-world datasets against network-embedding and graph-neural-network baselines, using 20, 40, and 60 labeled nodes per class.The test set contains 1000 nodes, and baselines are initialized and tuned for performance.
  • Node Classification: AM-GCN generally achieves the best performance across all datasets and label rates, with maximum ACC relative improvements of 8.59% on BlogCatalog and 8.63% on Flickr.It consistently outperforms both GCN and kNN-GCN.
  • Node Classification: Feature graphs outperform topology graphs on BlogCatalog, Flickr, and UAI2010, while AM-GCN improves more substantially on datasets with better feature graphs.These results support introducing feature graphs and using them for feature propagation and representation learning.
  • Ablation Study: AM-GCN outperforms its variants, and both consistency-only and disparity-only variants usually outperform the unconstrained model.The consistency constraint is generally more important than the disparity constraint.
  • Embedding Visualization: On BlogCatalog, AM-GCN embeddings show the most compact structure, highest intra-class similarity, and clearest class boundaries among the visualized methods.The comparison uses t-SNE visualizations of test-set embeddings colored by real labels.
  • Attention Mechanism: Attention values become larger for the more important information source, and training progressively differentiates topology, feature, and common embeddings.For BlogCatalog, topology attention decreases while feature attention increases during training.
  • Parameter Study: Performance is stable for γ from 1e-4 to 1e+4, whereas increasing β can cause a rapid drop beyond 1e-6 on Citeseer but remains relatively stable on BlogCatalog.For γ, performance first rises and then slowly declines as the coefficient increases.

5 RELATED WORK

Related work covers graph convolution models and analyzes how they combine topology and node features.

  • GCN Models: Existing GCN research includes spectral, Chebyshev, one-hop, attention-based, neighborhood-sampling, degree-aware, and multi-hop aggregation approaches.The section also discusses analyses showing smoothing and low-pass filtering effects in GCN fusion.
  • Fusion Analysis: Recent studies examine GCN fusion mechanisms, including Laplacian smoothing of node features and low-pass filtering induced by topology.These analyses motivate rethinking how topology and node features are integrated.

6 CONCLUSION

The paper identifies suboptimal topology-feature fusion in GCNs and proposes AM-GCN to learn suitable importance weights, with experiments showing superior performance on real-world datasets.

  • Conclusion: AM-GCN addresses the finding that existing GCN fusion of network topology and node features is distant from optimal.The paper frames adaptive extraction and fusion of correlated information as the central problem.
  • Conclusion: AM-GCN learns suitable importance weights when fusing topology and node-feature information through a multi-channel model.The proposed approach is designed to adaptively learn correlated information for classification.
  • Conclusion: Extensive experiments demonstrate superior performance over state-of-the-art models on real-world datasets.The conclusion reports this as evidence for the proposed model’s effectiveness.

A SUPPLEMENT

The supplement provides reproducibility materials and additional experiments supporting the paper’s conclusions.

  • Reproducibility: The supplement provides the experimental environment, websites for baselines and datasets, and detailed hyperparameter values.It also includes additional results supporting the paper’s conclusions.

A.1 Experiments Settings

The experiments use a fixed computing and software environment, with all experiments conducted under the stated setting.

  • All experiments are conducted with the following setting.
  • The experiments run on CentOS Linux 7.6.1810 with an Intel Xeon E5-2620 v4 CPU and GeForce GTX 1080 Ti GPU.
  • The software environment includes Python 3.7, PyTorch 1.1.0, NumPy 1.16.2, SciPy 1.3.1, NetworkX 2.4, and scikit-learn 0.21.3.

A.2 Baselines and Datasets

The paper identifies publicly available implementations for its baselines and provides URLs for the datasets used in the experiments.

  • Publicly available implementations of the baselines can be found at the listed URLs.
  • The listed baseline implementations include DeepWalk, LINE, Chebyshev, GCN, GAT, DEMO-Net, and MixHop.
  • The datasets used in the paper are also provided through the listed URLs.

A.3 Implementation Details

AM-GCN is implemented from a PyTorch version of Graph Convolutional Networks, with model parameter values documented for reproducibility.

  • The AM-GCN code is based on the Graph Convolutional Networks in PyTorch version 1.
  • The paper lists the parameter values used in AM-GCN.
  • The stated purpose of listing the model parameters is to support reproducibility.

A.4 Additional Results

Additional experiments examine attention trends and parameter behavior across datasets. The reported results support attention effectiveness and show that parameter effects depend on the constraint, dataset, and neighborhood size.

  • A.4 Additional Results: The additional experiments analyze attention trends on four datasets and parameter behavior on UAI2010 and Flickr.
  • A.4 Additional Results: On four additional datasets, attention values change consistently with Figure 5 and final values match the corresponding distributions in Figure 4.
  • A.4 Additional Results: Figures 10, 11, and 12 analyze γ, β, and k, respectively.
  • A.4 Additional Results: The additional-results section includes a model-hyperparameters table.
  • A.4 Additional Results: Consistency and disparity constraints remain stable across a large parameter range, although disparity performance may decrease beyond a suitable β boundary.
  • A.4 Additional Results: For UAI2010, performance first increases and then decreases as k varies from 2 to 10, whereas larger k benefits Flickr by adding richer feature-graph structure.
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