Topology Adaptive Graph Convolutional Networks
Abstract
Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provide a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution. The TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution as defined in graph signal processing. Since no approximation to the convolution is needed, TAGCN exhibits better performance than existing spectral CNNs on a number of data sets and is also computationally simpler than other recent methods.
Benchmark Results
Tested on 3 datasets
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphSAGE+CNA | 0.9418
±0.0033 | |
| 2 | GCN+CNA | 0.9366
±0.0048 | |
| 3 | TransformerConv | 0.9350
±0.0058 | |
| 21 | GCN | 0.9004 best reported | best at pub: Geometric deep learning on graphs and manifolds using mixture model CNNs (2016) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 39 | SAGE | 0.8911
±0.0012 | |
| 44 | GAT | 0.8897
±0.0014 best reported | |
| 139 | ChebNet | 0.8712
±0.0060 best reported | best today: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017) |
| 157 | DCNN | 0.8680 best reported | best at pub: Geometric deep learning on graphs and manifolds using mixture model CNNs (2016) best today: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 395 | TAGCN | 0.8330
±0.0070 | This paper |
| 435 | DeepWalk | 0.8290 best reported | best at pub: Geometric deep learning on graphs and manifolds using mixture model CNNs (2016) best today: Graph Representation Learning: A Survey (2019) |
| 508 | MoNet | 0.8220
±0.0070 best reported | best today: GRAND: Graph Neural Diffusion (ICML 2021) Difference within reported uncertainty; not counted as underperformance. |
| 724 | MLP | 0.7768 | |
| 762 | Planetoid | 0.7570 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 35 | GAT | 0.8080
±0.0026 best reported | best today: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 44 | GCN | 0.8033
±0.0088 best reported | |
| 61 | GraphSAGE | 0.7923
±0.0053 | |
| 232 | ChebNet | 0.7399
±0.0160 best reported | best today: Non-backtracking Graph Neural Networks (TMLR 2023) |
| 350 | MLP | 0.7289
±0.0010 | |
| 520 | TAGCN | 0.7140
±0.0050 | This paper |
| 692 | DeepWalk | 0.6785
±0.0079 best reported | best today: Decoupled Self-supervised Learning for Non-Homophilou Graphs (2022) |
| 782 | Planetoid | 0.6470 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 18 | GCN | 0.7900 | prev best: Geometric deep learning on graphs and manifolds using mixture model CNNs (2016) best today: Adaptive Tokenization: On the Hop-Overpriority Problem in Tokenized Graph Learning Models (2025) Improvement within reported uncertainty; not highlighted. |
| 20 | GAT | 0.9233
±0.0018 best reported | |
| 78 | DCNN | 0.8980 best reported | best at pub: Geometric deep learning on graphs and manifolds using mixture model CNNs (2016) best today: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 116 | SAGE | 0.8881
±0.0015 | |
| 199 | ChebNet | 0.8718
±0.0029 best reported | best today: Non-backtracking Graph Neural Networks (TMLR 2023) |
| 210 | MLP | 0.8690
±0.0074 | |
| 223 | DeepWalk | 0.8652
±0.0012 best reported | |
| 366 | TAGCN | 0.8110
±0.0040 | This paper |
| 446 | MoNet | 0.8006
±0.0055 best reported | |
| 727 | Planetoid | 0.7720 | This paper |
