Anonymous Walk Embeddings
Abstract
The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original problem of network representation in task-agnostic manner. Here, we coherently propose an approach for embedding entire graphs and show that our feature representations with SVM classifier increase classification accuracy of CNN algorithms and traditional graph kernels. For this we describe a recently discovered graph object, anonymous walk, on which we design task-independent algorithms for learning graph representations in explicit and distributed way. Overall, our work represents a new scalable unsupervised learning of state-of-the-art representations of entire graphs.
Benchmark Results
Tested on 3 datasets 1 baseline value reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
TU Dortmund
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | MSH-GNN | 0.9910
±0.0030 | |
| 2 | ID-GNN+BEC | 0.9830
±0.0360 | |
| 3 | SupCosine | 0.9830
±0.0250 | |
| 39 | GIN | 0.9330
±0.0290 | |
| 51 | PSCN | 0.9263
±0.0421 | This paper |
| 159 | WL | 0.9040
±0.0570 best reported | best at pub: On Valid Optimal Assignment Kernels and Applications to Graph Classification (NeurIPS 2016) best today: How Powerful are $K$-hop Message Passing Graph Neural Networks (NeurIPS 2022) |
| 341 | AWE | 0.8787
±0.0976 | This paper |
| 365 | DGK | 0.8744
±0.0272 best reported | best today: Model-Driven Graph Contrastive Learning (2025) |
| 403 | MLP | 0.8660
±0.0495 | |
| 506 | GK | 0.8350
±0.0060 best reported | best at pub: Learning Convolutional Neural Networks for Graphs (ICML 2016) best today: Supervised Contrastive Learning with Structure Inference for Graph Classification (2022) Difference within reported uncertainty; not counted as underperformance. |
| 614 | KR | 0.8005
±0.0164 | This paper |
| 752 | ER | 0.7189
±0.0066 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | WL-MLP | 0.9792 | |
| 2 | MSH-GNN | 0.9640
±0.0070 | |
| 3 | CoCN | 0.8722
±0.0013 | |
| 23 | GCN | 0.8260
±0.0220 | |
| 151 | MLP | 0.7920
±0.0240 | |
| 153 | WL | 0.7910
±0.0010 best reported | best at pub: On Valid Optimal Assignment Kernels and Applications to Graph Classification (NeurIPS 2016) Difference within reported uncertainty; not counted as underperformance. |
| 266 | AWE (DD) | 0.7393
±0.0194 | This paper |
| 267 | AWE (DD) RBF | 0.7393 | This paper |
| 269 | AWE (DD) Inner | 0.7377 | This paper |
| 274 | DGK | 0.7310
±0.0030 best reported | best at pub: Graph Capsule Convolutional Neural Networks (ICML 2018) best today: InfoGCL: Information-Aware Graph Contrastive Learning (NeurIPS 2021) Difference within reported uncertainty; not counted as underperformance. |
| 277 | GK | 0.7284
±0.0028 | This paper |
| 293 | AWE (FB) RBF | 0.7099 | This paper |
| 298 | AWE (DD) Poly | 0.7045 | This paper |
| 304 | AWE (FB) Inner | 0.6960 | This paper |
| 323 | AWE (FB) Poly | 0.6430 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GMN | 0.7866 | |
| 2 | MemGNN | 0.7550 | |
| 3 | TFGW SP | 0.7510
±0.0500 | |
| 17 | GatedGCN | 0.7000
±0.0494 | |
| 18 | WL | 0.6950
±0.0320 best reported | best at pub: Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (2017) best today: Template based Graph Neural Network with Optimal Transport Distances (NeurIPS 2022) |
| 26 | GraphSAGE | 0.6817
±0.0545 | |
| 124 | MLP | 0.5583
±0.0352 | |
| 145 | DGK | 0.5343
±0.0091 best reported | best at pub: Graph Capsule Convolutional Neural Networks (ICML 2018) |
| 169 | AWE | 0.4558
±0.0211 best reported | best today: Contrastive Graph Few-Shot Learning (2022) |
| 218 | GK | 0.3270
±0.0120 | prev best: Graph Capsule Convolutional Neural Networks (ICML 2018) |
| 232 | KR | 0.3001
±0.0101 | This paper |
| 303 | ER | 0.1497
±0.0028 | This paper |
