Semi-Supervised Classification with Graph Convolutional Networks

9 Sep 2016  ·  Thomas N. Kipf, Max Welling ·

We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification Chameleon (60%/20%/20% random splits) GCN 1:1 Accuracy 64.18 ± 2.62 # 18
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon(60%/20%/20% random splits) GCN 1:1 Accuracy 64.18 ± 2.62 # 17
Node Classification Citeseer GCN Accuracy 70.3 # 60
Node Classification CiteSeer (60%/20%/20% random splits) GCN 1:1 Accuracy 81.39 ± 1.23 # 15
Node Classification Cora GCN Accuracy 81.5% # 61
Node Classification Cora (60%/20%/20% random splits) GCN 1:1 Accuracy 87.78 ± 0.96 # 19
Node Classification on Non-Homophilic (Heterophilic) Graphs Cornell (60%/20%/20% random splits) GCN 1:1 Accuracy 82.46 ± 3.11 # 25
Node Classification Cornell (60%/20%/20% random splits) GCN 1:1 Accuracy 82.46 ± 3.11 # 25
Node Classification on Non-Homophilic (Heterophilic) Graphs Deezer-Europe GCN 1:1 Accuracy 62.23±0.53 # 21
Node Classification Film (60%/20%/20% random splits) GCN 1:1 Accuracy 35.51 ± 0.99 # 28
Node Classification Flickr GCN_cheby (Kipf and Welling, 2017) Accuracy 0.479 # 7
Node Classification Flickr GCN (Kipf and Welling, 2017) Accuracy 0.546 # 6
Node Classification genius GCN Accuracy 87.42 ± 0.37 # 14
Node Classification on Non-Homophilic (Heterophilic) Graphs genius GCN 1:1 Accuracy 87.42 ± 0.37 # 16
Node Classification NELL GCN Accuracy 66.0 # 2
Graph Property Prediction ogbg-code2 GCN Test F1 score 0.1507 ± 0.0018 # 18
Validation F1 score 0.1399 ± 0.0017 # 19
Number of params 11033210 # 12
Ext. data No # 1
Graph Property Prediction ogbg-code2 GCN+virtual node Test F1 score 0.1595 ± 0.0018 # 11
Validation F1 score 0.1461 ± 0.0013 # 12
Number of params 12484310 # 8
Ext. data No # 1
Graph Property Prediction ogbg-molhiv GCN Test ROC-AUC 0.7606 ± 0.0097 # 38
Validation ROC-AUC 0.8204 ± 0.0141 # 30
Number of params 527701 # 20
Ext. data No # 1
Graph Property Prediction ogbg-molhiv GCN (in Julia) Test ROC-AUC 0.7549 ± 0.0163 # 41
Validation ROC-AUC 0.8042 ± 0.0107 # 35
Number of params 527701 # 20
Ext. data No # 1
Graph Property Prediction ogbg-molhiv GCN+virtual node Test ROC-AUC 0.7599 ± 0.0119 # 39
Validation ROC-AUC 0.8384 ± 0.0091 # 12
Number of params 1978801 # 12
Ext. data No # 1
Graph Property Prediction ogbg-molpcba GCN+virtual node Test AP 0.2424 ± 0.0034 # 28
Validation AP 0.2495 ± 0.0042 # 26
Number of params 2017028 # 24
Ext. data No # 1
Graph Property Prediction ogbg-molpcba GCN Test AP 0.2020 ± 0.0024 # 34
Validation AP 0.2059 ± 0.0033 # 32
Number of params 565928 # 30
Ext. data No # 1
Graph Property Prediction ogbg-ppa GCN Test Accuracy 0.6839 ± 0.0084 # 15
Validation Accuracy 0.6497 ± 0.0034 # 14
Number of params 479437 # 15
Ext. data No # 1
Graph Property Prediction ogbg-ppa GCN+virtual node Test Accuracy 0.6857 ± 0.0061 # 14
Validation Accuracy 0.6511 ± 0.0048 # 13
Number of params 1930537 # 10
Ext. data No # 1
Link Property Prediction ogbl-citation2 Full-batch GCN Test MRR 0.8474 ± 0.0021 # 11
Validation MRR 0.8479 ± 0.0023 # 11
Number of params 296449 # 12
Ext. data No # 1
Link Property Prediction ogbl-collab GCN (val as input) Test Hits@50 0.4714 ± 0.0145 # 25
Validation Hits@50 0.5263 ± 0.0115 # 24
Number of params 296449 # 23
Ext. data No # 1
Link Property Prediction ogbl-collab GCN Test Hits@50 0.4475 ± 0.0107 # 27
Validation Hits@50 0.5263 ± 0.0115 # 24
Number of params 296449 # 23
Ext. data No # 1
Link Property Prediction ogbl-ddi GCN Test Hits@20 0.3707 ± 0.0507 # 23
Validation Hits@20 0.5550 ± 0.0208 # 23
Number of params 1289985 # 22
Ext. data No # 1
Link Property Prediction ogbl-ddi GCN+JKNet Test Hits@20 0.6056 ± 0.0869 # 19
Validation Hits@20 0.6776 ± 0.0095 # 18
Number of params 1421571 # 18
Ext. data No # 1
Link Property Prediction ogbl-ppa GCN Test Hits@100 0.1867 ± 0.0132 # 22
Validation Hits@100 0.1845 ± 0.0140 # 21
Number of params 278529 # 14
Ext. data No # 1
Node Property Prediction ogbn-arxiv GCN+residual+6 layers Test Accuracy 0.7286 ± 0.0016 # 51
Validation Accuracy 0.7382 ± 0.0007 # 54
Number of params 122542 # 63
Ext. data No # 1
Node Property Prediction ogbn-arxiv GCN Test Accuracy 0.7174 ± 0.0029 # 70
Validation Accuracy 0.7300 ± 0.0017 # 66
Number of params 110120 # 65
Ext. data No # 1
Node Property Prediction ogbn-arxiv GCN_res + 8 layers Test Accuracy 0.7262 ± 0.0037 # 56
Validation Accuracy 0.7369 ± 0.0021 # 55
Number of params 155824 # 58
Ext. data No # 1
Node Property Prediction ogbn-arxiv GCN+residual+node2vec Test Accuracy 0.7278 ± 0.0013 # 52
Validation Accuracy 0.7414 ± 0.0008 # 50
Number of params 21885098 # 7
Ext. data No # 1
Node Property Prediction ogbn-products Full-batch GCN Test Accuracy 0.7564 ± 0.0021 # 55
Validation Accuracy 0.9200 ± 0.0003 # 42
Number of params 103727 # 52
Ext. data No # 1
Node Property Prediction ogbn-proteins GCN Test ROC-AUC 0.7251 ± 0.0035 # 22
Validation ROC-AUC 0.7921 ± 0.0018 # 20
Number of params 96880 # 21
Ext. data No # 1
Graph Regression PCQM4Mv2-LSC GCN Validation MAE 0.1379 # 17
Test MAE 0.1398 # 12
Node Classification Penn94 GCN Accuracy 82.47 ± 0.27 # 12
Node Classification on Non-Homophilic (Heterophilic) Graphs Penn94 GCN 1:1 Accuracy 82.47 ± 0.27 # 11
Node Classification Pubmed GCN Accuracy 79.0 # 53
Node Classification PubMed (60%/20%/20% random splits) GCN 1:1 Accuracy 88.9 ± 0.32 # 22
Node Classification Squirrel (60%/20%/20% random splits) GCN 1:1 Accuracy 44.76 ± 1.39 # 22
Node Classification Texas (60%/20%/20% random splits) GCN 1:1 Accuracy 83.11 ± 3.2 # 24
Node Classification on Non-Homophilic (Heterophilic) Graphs Texas(60%/20%/20% random splits) GCN 1:1 Accuracy 83.11 ± 3.2 # 22
Node Classification on Non-Homophilic (Heterophilic) Graphs twitch-gamers GCN 1:1 Accuracy 62.18 ± 0.26 # 20
Node Classification Wisconsin (60%/20%/20% random splits) GCN 1:1 Accuracy 75.5 ± 2.92 # 26
Node Classification on Non-Homophilic (Heterophilic) Graphs Wisconsin(60%/20%/20% random splits) GCN 1:1 Accuracy 75.5 ± 2.92 # 23

Results from Other Papers


Task Dataset Model Metric Name Metric Value Rank Source Paper Compare
Node Classification Brazil Air-Traffic GCN_cheby (Kipf and Welling, 2017) Accuracy 0.516 # 3
Node Classification Europe Air-Traffic GCN (Kipf and Welling, 2017) Accuracy 37.1 # 6
Node Classification Europe Air-Traffic GCN_cheby (Kipf and Welling, 2017) Accuracy 46.0 # 2
Node Classification Facebook GCN (Kipf and Welling, 2017) Accuracy 57.5 # 4
Node Classification Facebook GCN_cheby (Kipf and Welling, 2017) Accuracy 64.6 # 2
Node Classification Wiki-Vote GCN_cheby (Kipf and Welling, 2017) Accuracy 49.5 # 3
Node Classification Wiki-Vote GCN (Kipf and Welling, 2017) Accuracy 32.9 # 5

Methods