Feature Expansion for Graph Neural Networks
Abstract
Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.
Benchmark Results
Tested on 8 datasets 8 baseline values reported too low Non-standard metric on 4 datasets
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
Cora
Global leaderboard →| # | Model | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|
| 1 | FE-GNN (C) | 0.8945
±0.0022 | This paper |
CiteSeer
Global leaderboard →Default metric is Accuracy. The paper reports 11 values on Accuracy and 1 value on Accuracy (micro F1 per L1108) .
| # | Model | Accuracy ↑ default | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|---|
| 1 | CNA | 0.9575
±
0.0058 | — | Accuracy (micro F1 per L1108)
— |
| 2 | IS-GIB | 0.9390
±
0.0187 | — | Accuracy (micro F1 per L1108)
— |
| 3 | EERM | 0.9112
±
0.0145 | — | Accuracy (micro F1 per L1108)
— |
| 15 | GNN-LF | 0.8366
±
0.0006 | — | Accuracy (micro F1 per L1108)
— |
| 16 | GNN-HF | 0.8356
±
0.0010 | — | Accuracy (micro F1 per L1108)
— |
| 18 | FE-GNN (C) | —
| 0.8196
±
0.0023 | Accuracy (micro F1 per L1108)
0.8196
±
0.0023 |
| 20 | APPNP | 0.8142
±0.0026 | — | Accuracy (micro F1 per L1108)
— prev best: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 32 | GPRGNN | 0.7857
±0.0031 | — | Accuracy (micro F1 per L1108)
— |
| 35 | GAT | 0.8080
±0.0026 | — | Accuracy (micro F1 per L1108)
— prev best: Gophormer: Ego-Graph Transformer for Node Classification (2021) Improvement within reported uncertainty; not highlighted. |
| 36 | GCNII | 0.8076
±0.0030 | — | Accuracy (micro F1 per L1108)
— |
| 44 | GCN | 0.8033
±0.0088 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) Difference within reported uncertainty; not counted as underperformance. |
| 58 | BernNet | 0.7934
±0.0032 | — | Accuracy (micro F1 per L1108)
— prev best: Uplifting Message Passing Neural Network with Graph Original Information (2022) |
| 59 | ADA-UGNN | 0.7934
±
0.0009 | — | Accuracy (micro F1 per L1108)
— |
| 61 | GraphSAGE | 0.7923
±0.0053 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) Difference within reported uncertainty; not counted as underperformance. |
| 90 | ChebyNet | 0.7797
±0.0036 | — | Accuracy (micro F1 per L1108)
— prev best: Spectral Graph Attention Network with Fast Eigen-approximation (2020) |
| 259 | SAGE | 0.7361
±
0.0190 | — | Accuracy (micro F1 per L1108)
— |
| 350 | MLP | 0.7289
±
0.0010 | — | Accuracy (micro F1 per L1108)
— |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 17 | APPNP | 0.9355
±0.0060 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 18 | GCN | 0.9296
±0.0015 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 20 | GAT | 0.9233
±0.0018 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 68 | ADA-UGNN | 0.9008
±0.0005 | This paper |
| 93 | BernNet | 0.8933
±0.0007 | prev best: Uplifting Message Passing Neural Network with Graph Original Information (2022) |
| 101 | GPRGNN | 0.8911
±0.0008 | |
| 107 | ChebyNet | 0.8904
±0.0008 | prev best: Spectral Graph Attention Network with Fast Eigen-approximation (2020) |
| 116 | SAGE | 0.8881
±0.0015 | |
| 125 | GraphSAGE | 0.8765
±0.0014 | prev best: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) best today: Non-backtracking Graph Neural Networks (TMLR 2023) |
| 163 | GNN-HF | 0.8783
±0.0010 | This paper |
| 168 | GNN-LF | 0.8779
±0.0005 | This paper |
| 210 | MLP | 0.8690
±0.0074 best reported | best at pub: Block Modeling-Guided Graph Convolutional Neural Networks (AAAI 2021) best today: On the Equivalence of Graph Convolution and Mixup (TMLR 2023) |
Amazon-Photo
Global leaderboard →Default metric is Accuracy. The paper reports 1 value on Accuracy and 1 value on Accuracy (micro F1 per L1108) .
| # | Model | Accuracy ↑ default | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|---|
| 1 | GraphTARIF | 0.9703
±
0.0019 | — | Accuracy (micro F1 per L1108)
— |
| 2 | GAT | 0.9669
±
0.0014 | — | Accuracy (micro F1 per L1108)
— |
| 3 | GAT+T | 0.9660
±
0.0007 | — | Accuracy (micro F1 per L1108)
— |
| 7 | SAGE | 0.9643
±
0.0027 | — | Accuracy (micro F1 per L1108)
— |
| 38 | FE-GNN (C) | —
| 0.9536
±
0.0014 | Accuracy (micro F1 per L1108)
0.9536
±
0.0014 |
| 68 | C (orthogonal) | 0.9484
±
0.0079 | — | Accuracy (micro F1 per L1108)
— |
| 390 | MLP | 0.9128
±
0.0063 | — | Accuracy (micro F1 per L1108)
— |
Amazon-Computers
Global leaderboard →| # | Model | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|
| 1 | FE-GNN (C) | 0.9079
±0.0008 | This paper |
Heterophilic Graphs
Actor
Global leaderboard →Default metric is Accuracy. The paper reports 8 values on Accuracy and 5 values on Accuracy (micro F1 per L1108) .
| # | Model | Accuracy ↑ default | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|---|
| 1 | DiGGR | 0.4535
±
0.0353 | — | Accuracy (micro F1 per L1108)
— |
| 2 | TRIGON | 0.4402
±
0.0028 | — | Accuracy (micro F1 per L1108)
— |
| 3 | DoG | 0.4320
±
0.0120 | — | Accuracy (micro F1 per L1108)
— |
| 11 | GNN-HF | —
| 0.4247
±
0.0007 | Accuracy (micro F1 per L1108)
0.4247
±
0.0007 |
| 17 | GNN-LF | 0.4197
±
0.0006 | — | Accuracy (micro F1 per L1108)
— |
| 29 | ADA-UGNN | —
| 0.4138
±
0.0012 | Accuracy (micro F1 per L1108)
0.4138
±
0.0012 |
| 38 | GCNII | 0.3861
±0.0026 | — | Accuracy (micro F1 per L1108)
— prev best: Understanding convolution on graphs via energies (TMLR 2022) Improvement within reported uncertainty; not highlighted. |
| 40 | FE-GNN (C) | —
| 0.4054
±
0.0015 | Accuracy (micro F1 per L1108)
0.4054
±
0.0015 |
| 41 | APPNP | 0.3990
±0.0025 | — | Accuracy (micro F1 per L1108)
— prev best: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) best today: A Quasi-Wasserstein Loss for Learning Graph Neural Networks (WWW 2023) Improvement within reported uncertainty; not highlighted. |
| 42 | MLP | 0.4026
±0.0108 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Heterophily-Aware Graph Attention Network (2023) Difference within reported uncertainty; not counted as underperformance. |
| 64 | ChebyNet | 0.3917
±0.0143 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 68 | GraphSAGE | 0.3899
±0.0085 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Hierarchical Graph Transformer with Adaptive Node Sampling (NeurIPS 2022) best today: A Quasi-Wasserstein Loss for Learning Graph Neural Networks (WWW 2023) |
| 52 | GPRGNN | —
| 0.3693
±
0.0026 | Accuracy (micro F1 per L1108)
0.3693
±
0.0026 |
| 135 | GCN | 0.3690 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 21 | BernNet | —
| 0.3689
±
0.0030 | Accuracy (micro F1 per L1108)
0.3689
±
0.0030 |
| 182 | GAT | 0.3605
±0.0035 best reported | — | Accuracy (micro F1 per L1108)
— best at pub: Hierarchical Graph Transformer with Adaptive Node Sampling (NeurIPS 2022) |
| 266 | GIN | 0.3410
±
0.0030 | — | Accuracy (micro F1 per L1108)
— |
Chameleon
Global leaderboard →| # | Model | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|
| 1 | FE-GNN (C) | 0.7333
±0.0035 | This paper |
Squirrel
Global leaderboard →| # | Model | Accuracy (micro F1 per L1108) ↑ | Paper |
|---|---|---|---|
| 1 | FE-GNN (M) | 0.6790
±0.0023 | This paper |
