Contrastive Learning for Non-Local Graphs with Multi-Resolution Structural Views
Abstract
Learning node-level representations of heterophilic graphs is crucial for various applications, including fraudster detection and protein function prediction. In such graphs, nodes share structural similarity identified by the equivalence of their connectivity which is implicitly encoded in the form of higher-order hierarchical information in the graphs. The contrastive methods are popular choices for learning the representation of nodes in a graph. However, existing contrastive methods struggle to capture higher-order graph structures. To address this limitation, we propose a novel multiview contrastive learning approach that integrates diffusion filters on graphs. By incorporating multiple graph views as augmentations, our method captures the structural equivalence in heterophilic graphs, enabling the discovery of hidden relationships and similarities not apparent in traditional node representations. Our approach outperforms baselines on synthetic and real structural datasets, surpassing the best baseline by $16.06\
Benchmark Results
Tested on 4 datasets 7 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Heterophilic Graphs
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9672
±0.0147 | |
| 2 | DoG | 0.9660
±0.0210 | |
| 3 | GPF-plus | 0.9583
±0.0419 | |
| 34 | MLP | 0.9230
±0.0070 | |
| 53 | GraphSAGE | 0.9000
±0.0365 | |
| 304 | DGI | 0.7581
±0.0503 best reported | |
| 351 | MVGRL | 0.7301
±0.0552 best reported | |
| 358 | Ours (dedicated) | 0.7289
±0.0660 | This paper |
| 396 | NWR-GAE | 0.6962
±0.0666 | This paper |
| 523 | VGAE | 0.5920 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) |
| 526 | GAE | 0.5909
±0.1626 best reported | best at pub: Multi-View Graph Representation Learning Beyond Homophily (2023) Difference within reported uncertainty; not counted as underperformance. |
| 585 | struc2vec | 0.4931
±0.0322 best reported | best at pub: Decoupled Self-supervised Learning for Non-Homophilou Graphs (2022) Difference within reported uncertainty; not counted as underperformance. |
| 589 | GraphCL | 0.4867
±0.0437 best reported | best at pub: Decoupled Self-supervised Learning for Non-Homophilou Graphs (2022) Difference within reported uncertainty; not counted as underperformance. |
| 590 | Node2Vec | 0.4864
±0.0292 | This paper |
| 595 | DeepWalk | 0.4700
±0.2928 best reported | best at pub: Multi-View Graph Representation Learning Beyond Homophily (2023) Difference within reported uncertainty; not counted as underperformance. |
| 603 | ARGVA | 0.4324
±0.0538 | This paper |
| 605 | RolX | 0.4256
±0.0713 | This paper |
| 613 | GraphWave | 0.3745
±0.0709 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9541
±0.0272 | |
| 2 | ACM-GCN | 0.9480
±0.0380 | |
| 3 | RF-GCN | 0.9429 | |
| 24 | MLP | 0.9136
±0.0070 | |
| 138 | SAGE | 0.8269 | |
| 236 | mechanism (shared) | 0.7470
±0.0756 | This paper |
| 340 | MVGRL | 0.6430 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) |
| 350 | DGI | 0.6335 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) |
| 354 | GAE | 0.6309
±0.0987 best reported | best at pub: Multi-View Graph Representation Learning Beyond Homophily (2023) |
| 386 | VGAE | 0.5919 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 394 | NWR-GAE | 0.5864
±0.0561 | This paper |
| 500 | DeepWalk | 0.4867
±0.2784 best reported | best at pub: Multi-View Graph Representation Learning Beyond Homophily (2023) Difference within reported uncertainty; not counted as underperformance. |
| 513 | GraphCL | 0.4722
±0.0450 best reported | best at pub: Decoupled Self-supervised Learning for Non-Homophilou Graphs (2022) Difference within reported uncertainty; not counted as underperformance. |
| 524 | GraphWave | 0.4596
±0.0220 | This paper |
| 542 | Node2Vec | 0.4294 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 551 | ARGVA | 0.4108
±0.0485 | This paper |
| 571 | struc2vec | 0.3022
±0.0587 best reported | best at pub: Decoupled Self-supervised Learning for Non-Homophilou Graphs (2022) Difference within reported uncertainty; not counted as underperformance. |
| 575 | RolX | 0.2567
±0.1178 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DiGGR | 0.4535
±0.0353 | |
| 2 | TRIGON | 0.4402
±0.0028 | |
| 3 | DoG | 0.4320
±0.0120 | |
| 42 | MLP | 0.4026
±0.0108 | |
| 68 | GraphSAGE | 0.3899
±0.0085 | |
| 184 | mechanism (dedicated) | 0.3601
±0.0068 | This paper |
| 247 | MVGRL | 0.3464
±0.0020 best reported | best at pub: Augmentation-Free Graph Contrastive Learning with Performance Guarantee (2022) best today: Frequency-Corrupt Based Graph Self-Supervised Learning (WWW 2026) |
| 309 | VGAE | 0.3157
±0.0075 best reported | best at pub: Augmentation-Free Graph Contrastive Learning with Performance Guarantee (2022) best today: Frequency-Corrupt Based Graph Self-Supervised Learning (WWW 2026) |
| 310 | GraphCL | 0.3151
±0.0154 best reported | best today: Toward General Digraph Contrastive Learning: A Dual Spatial Perspective (2025) |
| 335 | DGI | 0.3067
±0.0063 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) best today: Toward General Digraph Contrastive Learning: A Dual Spatial Perspective (2025) |
| 348 | NWR-GAE | 0.3017
±0.0017 | This paper |
| 374 | ARGVA | 0.2897
±0.0117 | This paper |
| 383 | GAE | 0.2863
±0.0105 | prev best: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Improvement within reported uncertainty; not highlighted. |
| 390 | Node2Vec | 0.2828 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) |
| 409 | GraphWave | 0.2729
±0.0309 | This paper |
| 424 | DeepWalk | 0.2550
±0.0028 best reported | best at pub: Augmentation-Free Graph Contrastive Learning with Performance Guarantee (2022) Difference within reported uncertainty; not counted as underperformance. |
| 428 | RolX | 0.2542
±0.0055 | This paper |
| 434 | struc2vec | 0.2513
±0.0079 | This paper |
Hypergraph Benchmarks
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | HealHGNN | 0.7718
±0.0235 | |
| 2 | Deep-HGNN | 0.7526
±0.0176 | |
| 3 | mechanism (shared) | 0.7470
±0.0756 | This paper |
| 12 | MLP | 0.6793
±0.0233 | |
| 20 | NWR-GAE | 0.5864
±0.0561 | This paper |
| 21 | MVGRL | 0.5351
±0.0326 | This paper |
| 22 | VGAE | 0.4932
±0.0919 | This paper |
| 23 | DGI | 0.4648
±0.0797 | This paper |
| 24 | GraphWave | 0.4596
±0.0220 | This paper |
| 25 | GAE | 0.4540
±0.0999 | This paper |
| 26 | GraphCL | 0.4486
±0.0373 | This paper |
| 27 | DeepWalk | 0.4121
±0.0340 | This paper |
| 28 | ARGVA | 0.4108
±0.0485 | This paper |
| 29 | Node2Vec | 0.4054
±0.0162 | This paper |
| 30 | RolX | 0.2567
±0.1178 | This paper |
| 31 | struc2vec | 0.2372
±0.1369 | This paper |
