Learning to Drop: Robust Graph Neural Network via Topological Denoising
Abstract
Graph Neural Networks (GNNs) have shown to be powerful tools for graph analytics. The key idea is to recursively propagate and aggregate information along edges of the given graph. Despite their success, however, the existing GNNs are usually sensitive to the quality of the input graph. Real-world graphs are often noisy and contain task-irrelevant edges, which may lead to suboptimal generalization performance in the learned GNN models. In this paper, we propose PTDNet, a parameterized topological denoising network, to improve the robustness and generalization performance of GNNs by learning to drop task-irrelevant edges. PTDNet prunes task-irrelevant edges by penalizing the number of edges in the sparsified graph with parameterized networks. To take into consideration of the topology of the entire graph, the nuclear norm regularization is applied to impose the low-rank constraint on the resulting sparsified graph for better generalization. PTDNet can be used as a key component in GNN models to improve their performances on various tasks, such as node classification and link prediction. Experimental studies on both synthetic and benchmark datasets show that PTDNet can improve the performance of GNNs significantly and the performance gain becomes larger for more noisy datasets.
Benchmark Results
Tested on 4 datasets 3 baseline values reported too low
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: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 39 | SAGE | 0.8911
±0.0012 | |
| 43 | DropEdge | 0.8900 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) Difference within reported uncertainty; not counted as underperformance. |
| 44 | GAT | 0.8897
±0.0014 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 141 | GraphSAGE | 0.8708
±0.0085 best reported | best at pub: The Impact of Global Structural Information in Graph Neural Networks Applications (2020) best today: Large Language Model Meets Graph Neural Network in Knowledge Distillation (AAAI 2024) |
| 260 | PTDNet | 0.8440
±0.0230 | This paper |
| 326 | PTDNet-wl | 0.8370
±0.0220 | This paper |
| 383 | NeuralSparse | 0.8340
±0.0150 | This paper |
| 724 | MLP | 0.7768 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 44 | GCN | 0.8033
±0.0088 | |
| 252 | GAT PTDNet | 0.7370
±0.0310 | This paper |
| 350 | MLP | 0.7289
±0.0010 | |
| 366 | GCN PTDNet | 0.7270
±0.0180 | This paper |
| 413 | GAT NeuralSparse | 0.7240
±0.0260 | This paper |
| 431 | GAT PTDNet-wl | 0.7230
±0.0140 | This paper |
| 439 | GCN DropEdge | 0.7220
±0.0320 | This paper |
| 450 | GAT Basic | 0.7210
±0.0090 | This paper |
| 485 | GCN PTDNet-wl | 0.7170
±0.1700 | This paper |
| 510 | GCN NeuralSparse | 0.7150
±0.0140 | This paper |
| 563 | GAT DropEdge | 0.7090
±0.0200 | This paper |
| 605 | GCN Basic | 0.7030
±0.0120 | This paper |
| 689 | GraphSage PTDNet | 0.6790
±0.0180 | This paper |
| 695 | GraphSage PTDNet-wl | 0.6780
±0.0220 | This paper |
| 700 | GraphSage Basic | 0.6760
±0.0230 | This paper |
| 705 | GraphSage NeuralSparse | 0.6740
±0.0110 | This paper |
| 721 | GraphSage DropEdge | 0.6700
±0.0310 | 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 | 0.9296
±0.0015 | |
| 210 | MLP | 0.8690
±0.0074 | |
| 479 | GCN PTDNet | 0.7980
±0.0240 | This paper |
| 545 | GAT PTDNet | 0.7930
±0.0150 | This paper |
| 561 | GAT PTDNet-wl | 0.7920
±0.0140 | This paper |
| 577 | GCN PTDNet-wl | 0.7910
±0.0120 | This paper |
| 590 | GCN Basic | 0.7900
±0.0200 | This paper |
| 591 | GAT Basic | 0.7900
±0.0080 | This paper |
| 617 | GCN NeuralSparse | 0.7880
±0.0180 | This paper |
| 637 | GCN DropEdge | 0.7850
±0.0430 | This paper |
| 677 | GAT NeuralSparse | 0.7800
±0.0170 | This paper |
| 689 | GAT DropEdge | 0.7790
±0.0190 | This paper |
| 734 | GraphSage PTDNet | 0.7710
±0.0100 | This paper |
| 741 | GraphSage PTDNet-wl | 0.7700
±0.0240 | This paper |
| 752 | GraphSage Basic | 0.7670
±0.0200 | This paper |
| 797 | GraphSage NeuralSparse | 0.7510
±0.0210 | This paper |
| 802 | GraphSage DropEdge | 0.7480
±0.0260 | This paper |
| # | Model | F1 ↑ | Paper |
|---|---|---|---|
| 1 | GAMLP(JK) | 0.9982
±0.0001 | |
| 2 | GraphCON-GCN | 0.9960 | |
| 3 | GCNII | 0.9953
±0.0001 | |
| 21 | GCN | 0.9850 | |
| 35 | GAT PTDNet | 0.9800
±0.0220 | This paper |
| 43 | GAT PTDNet-wl | 0.9780
±0.0180 | This paper |
| 61 | GAT Basic | 0.9730
±0.0120 | This paper |
| 88 | GAT NeuralSparse | 0.9210
±0.0180 | This paper |
| 95 | GAT DropEdge | 0.8500
±0.0380 | This paper |
| 99 | GCN PTDNet | 0.8030
±0.0080 | This paper |
| 110 | GCN PTDNet-wl | 0.7520
±0.0170 | This paper |
| 139 | GCN Basic | 0.6600
±0.0240 | This paper |
| 141 | GCN NeuralSparse | 0.6510
±0.0140 | This paper |
| 144 | GraphSage PTDNet | 0.6480
±0.0250 | This paper |
| 147 | GraphSage PTDNet-wl | 0.6450
±0.0200 | This paper |
| 150 | GraphSage NeuralSparse | 0.6260
±0.0230 | This paper |
| 153 | GraphSage Basic | 0.6180
±0.0140 | This paper |
| 155 | GraphSage DropEdge | 0.6100
±0.0350 | This paper |
| 156 | GCN DropEdge | 0.6060
±0.0410 | This paper |
| 173 | MLP | 0.4620 |
