Prototypical Graph Contrastive Learning

Shuai Lin, Pan Zhou, Zi-Yuan Hu, Shuojia Wang, Ruihui Zhao, Yefeng Zheng, Liang Lin, E. Xing, Xiaodan Liang

Main figure for Prototypical Graph Contrastive Learning

Abstract

Graph-level representations are critical in various real-world applications, such as predicting the properties of molecules. But in practice, precise graph annotations are generally very expensive and time-consuming. To address this issue, graph contrastive learning constructs instance discrimination task which pulls together positive pairs (augmentation pairs of the same graph) and pushes away negative pairs (augmentation pairs of different graphs) for unsupervised representation learning. However, since for a query, its negatives are uniformly sampled from all graphs, existing methods suffer from the critical sampling bias issue, i.e., the negatives likely having the same semantic structure with the query, leading to performance degradation. To mitigate this sampling bias issue, in this paper, we propose a Prototypical Graph Contrastive Learning (PGCL) approach. Specifically, PGCL models the underlying semantic structure of the graph data via clustering semantically similar graphs into the same group, and simultaneously encourages the clustering consistency for different augmentations of the same graph. Then given a query, it performs negative sampling via drawing the graphs from those clusters that differ from the cluster of query, which ensures the semantic difference between query and its negative samples. Moreover, for a query, PGCL further reweights its negative samples based on the distance between their prototypes (cluster centroids) and the query prototype such that those negatives having moderate prototype distance enjoy relatively large weights. This reweighting strategy is proved to be more effective than uniform sampling. Experimental results on various graph benchmarks testify the advantages of our PGCL over state-of-the-art methods. Code is publicly available at https://github.com/ha-lins/PGCL.

Proposed method: PGCL

Benchmark Results

Tested on 4 datasets 10 baseline values reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

TU Dortmund

#ModelAccuracy ↑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
63
GCN
actual #63 vs paper #432 369 places worse
0.9220 ±0.0440
best reported
actual #63 vs paper #432 369 places worse
paper 0.8560 ±0.0580

Difference within reported uncertainty; not counted as underperformance.

paper 0.8560 ±0.0580 Δ at pub 0.0350 Δ today 0.0660
106
PGCL
0.9110 ±0.0120
This paper
158
GraphSAGE
actual #158 vs paper #446 288 places worse
0.9040 ±0.0780
best reported
actual #158 vs paper #446 288 places worse
paper 0.8510 ±0.0760

Difference within reported uncertainty; not counted as underperformance.

paper 0.8510 ±0.0760 Δ at pub 0.0060 Δ today 0.0530
159
WL
actual #159 vs paper #597 438 places worse
0.9040 ±0.0570
best reported
actual #159 vs paper #597 438 places worse
paper 0.8070 ±0.0300
paper 0.8070 ±0.0300 Δ at pub 0.0550 Δ today 0.0970
199
MVGRL
actual #199 vs paper #213 14 places worse
0.8993 ±0.0616
best reported
actual #199 vs paper #213 14 places worse
paper 0.8970 ±0.0110

Difference within reported uncertainty; not counted as underperformance.

paper 0.8970 ±0.0110 Δ today 0.0023
238
GIN-0
0.8940 ±0.0560
This paper
257
InfoGraph
actual #257 vs paper #272 15 places worse
0.8930 ±0.0514
best reported
actual #257 vs paper #272 15 places worse
paper 0.8900 ±0.0110
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8900 ±0.0110 Δ at pub 0.0001 Δ today 0.0030
274
GIN-ε
0.8900 ±0.0600
This paper
332
MLG
actual #332 vs paper #334 2 places worse
0.8794 ±0.0161
best reported
actual #332 vs paper #334 2 places worse
paper 0.8790 ±0.0160
best at pub: The Multiscale Laplacian Graph Kernel (NeurIPS 2016)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8790 ±0.0160 Δ at pub 0.0004
354
GraphCL
actual #354 vs paper #396 42 places worse
0.8766 ±0.0103
best reported
actual #354 vs paper #396 42 places worse
paper 0.8680 ±0.0130
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8680 ±0.0130 Δ today 0.0086
365
DGK
actual #365 vs paper #366 1 place worse
0.8744 ±0.0272
best reported
actual #365 vs paper #366 1 place worse
paper 0.8740 ±0.0270
best at pub: Provably Powerful Graph Networks (NeurIPS 2019)

Difference within reported uncertainty; not counted as underperformance.

paper 0.8740 ±0.0270 Δ at pub 0.0004 Δ today 0.0004
381
GCKN
0.8720 ±0.0680
This paper
403
MLP
0.8660 ±0.0495
407
graph2vec
actual #407 vs paper #515 108 places worse
0.8644 ±0.0125
best reported
actual #407 vs paper #515 108 places worse
paper 0.8320 ±0.0930

Difference within reported uncertainty; not counted as underperformance.

paper 0.8320 ±0.0930 Δ at pub 0.0048 Δ today 0.0324
408
GCC
0.8640 ±0.0050
This paper
444
GL
actual #444 vs paper #575 131 places worse
0.8520 ±0.0090
best reported
actual #444 vs paper #575 131 places worse
paper 0.8170 ±0.0210
paper 0.8170 ±0.0210 Δ at pub 0.0350
#ModelAccuracy ↑Paper
1
WL-MLP
0.9954
2
GIN
0.9934
3
GCN
actual #3 vs paper #214 211 places worse
0.9727
best reported
actual #3 vs paper #214 211 places worse
paper 0.8020 ±0.0200
best at pub: Hierarchical Graph Capsule Network (AAAI 2020)
paper 0.8020 ±0.0200 Δ at pub 0.0345 Δ today 0.1707
12
WL
actual #12 vs paper #223 211 places worse
0.8590 ±0.0010
best reported
actual #12 vs paper #223 211 places worse
paper 0.8000 ±0.0050
best at pub: Propagation Kernels (2014)
paper 0.8000 ±0.0050 Δ at pub 0.0590
92
GIN-0
0.8270 ±0.0170
This paper
94
GIN-ε
0.8270 ±0.0160
This paper
104
GraphCL
actual #104 vs paper #325 221 places worse
0.7790 ±0.0040
actual #104 vs paper #325 221 places worse
paper 0.7790 ±0.0040

Improvement within reported uncertainty; not highlighted.

paper 0.7790 ±0.0040 Δ at pub 0.0003 Δ today 0.0460
131
GraphSAGE
actual #131 vs paper #329 198 places worse
0.8200 ±0.0100
best reported
actual #131 vs paper #329 198 places worse
paper 0.7770 ±0.0150
210
DGK
actual #210 vs paper #211 1 place worse
0.8031 ±0.0046
best reported
actual #210 vs paper #211 1 place worse
paper 0.8030 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.8030 ±0.0050 Δ at pub 0.0001 Δ today 0.0001
257
GCKN
actual #257 vs paper #476 219 places worse
0.7920 ±0.0120
best reported
actual #257 vs paper #476 219 places worse
paper 0.7060 ±0.0200
paper 0.7060 ±0.0200 Δ today 0.0860
273
PGCL
0.7880 ±0.0080
This paper
338
InfoGraph
actual #338 vs paper #440 102 places worse
0.7750 ±0.0074
best reported
actual #338 vs paper #440 102 places worse
paper 0.7380 ±0.0070
paper 0.7380 ±0.0070 Δ at pub 0.0284 Δ today 0.0370
356
MVGRL
actual #356 vs paper #410 54 places worse
0.7700 ±0.0080
best reported
actual #356 vs paper #410 54 places worse
paper 0.7500 ±0.0070
paper 0.7500 ±0.0070 Δ today 0.0200
406
graph2vec
actual #406 vs paper #446 40 places worse
0.7540 ±0.0120
best reported
actual #406 vs paper #446 40 places worse
paper 0.7320 ±0.0180
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7320 ±0.0180 Δ at pub 0.0002 Δ today 0.0220
478
GL
actual #478 vs paper #574 96 places worse
0.7050 ±0.0020
best reported
actual #478 vs paper #574 96 places worse
paper 0.5390 ±0.0040
paper 0.5390 ±0.0040 Δ at pub 0.1660
512
GCC
0.6690 ±0.0020
This paper
#ModelAccuracy ↑Paper
1
WL-MLP
0.9792
2
MSH-GNN
0.9640 ±0.0070
3
CoCN
0.8722 ±0.0013
23
GCN
actual #23 vs paper #156 133 places worse
0.8260 ±0.0220
best reported
actual #23 vs paper #156 133 places worse
paper 0.7900 ±0.0180
paper 0.7900 ±0.0180 Δ at pub 0.0160 Δ today 0.0360
30
GIN
0.8220 ±0.0210
75
GCC
actual #75 vs paper #249 174 places worse
0.8110
best reported
actual #75 vs paper #249 174 places worse
paper 0.7520 ±0.0030
paper 0.7520 ±0.0030 Δ at pub 0.0590
80
GraphCL
actual #80 vs paper #289 209 places worse
0.8108 ±0.0017
best reported
actual #80 vs paper #289 209 places worse
paper 0.7140 ±0.0120
paper 0.7140 ±0.0120 Δ today 0.0968
104
MVGRL
actual #104 vs paper #307 203 places worse
0.8048 ±0.0029
best reported
actual #104 vs paper #307 203 places worse
paper 0.6890 ±0.0190
paper 0.6890 ±0.0190 Δ today 0.1158
112
GIN-0
0.8020 ±0.0190
This paper
120
GIN-ε
actual #120 vs paper #120
0.8010 ±0.0190
actual #120 vs paper #120
paper 0.8010 ±0.0190

Improvement within reported uncertainty; not highlighted.

paper 0.8010 ±0.0190 Δ at pub 0.0030
146
InfoGraph
actual #146 vs paper #312 166 places worse
0.7940
best reported
actual #146 vs paper #312 166 places worse
paper 0.6760 ±0.0120
paper 0.6760 ±0.0120 Δ at pub 0.1180
151
MLP
0.7920 ±0.0240
228
PGCL
0.7600 ±0.0030
This paper
260
GCKN
actual #260 vs paper #342 82 places worse
0.7430 ±0.0280
best reported
actual #260 vs paper #342 82 places worse
paper 0.5430 ±0.0100
paper 0.5430 ±0.0100 Δ today 0.2000
321
GL
actual #321 vs paper #338 17 places worse
0.6470 ±0.0010
best reported
actual #321 vs paper #338 17 places worse
paper 0.5630 ±0.0060
paper 0.5630 ±0.0060 Δ at pub 0.0840
#ModelAccuracy ↑Paper
1
OEPG
0.9630 ±0.0090
2
MSH-GNN
0.9580 ±0.0090
3
GNN-AK+
0.9480 ±0.0080
12
GIN-0
0.9240 ±0.0250
This paper
13
GIN
0.9240 ±0.0250
19
GIN-ε
0.9220 ±0.0230
This paper
23
GraphCL
actual #23 vs paper #44 21 places worse
0.9169 ±0.0070
best reported
actual #23 vs paper #44 21 places worse
paper 0.8950 ±0.0080
best at pub: Graph Contrastive Learning Automated (ICML 2021)
paper 0.8950 ±0.0080 Δ at pub 0.0003 Δ today 0.0219
25
PGCL
0.9150 ±0.0070
This paper
42
GCC
actual #42 vs paper #50 8 places worse
0.8980
best reported
actual #42 vs paper #50 8 places worse
paper 0.8840 ±0.0030
paper 0.8840 ±0.0030 Δ at pub 0.0140
46
InfoGraph
actual #46 vs paper #68 22 places worse
0.8939 ±0.0181
best reported
actual #46 vs paper #68 22 places worse
paper 0.8250 ±0.0140
paper 0.8250 ±0.0140 Δ today 0.0689
65
MVGRL
0.8450 ±0.0060
This paper
73
DGK
actual #73 vs paper #73
0.7804 ±0.0039
best reported
actual #73 vs paper #73
paper 0.7800 ±0.0040
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7800 ±0.0040 Δ at pub 0.0004 Δ today 0.0004
75
GL
actual #75 vs paper #76 1 place worse
0.7734 ±0.0018
best reported
actual #75 vs paper #76 1 place worse
paper 0.7730 ±0.0020
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7730 ±0.0020 Δ at pub 0.0004 Δ today 0.0004
80
graph2vec
actual #80 vs paper #80
0.7580 ±0.0100
actual #80 vs paper #80
paper 0.7580 ±0.0100

Improvement within reported uncertainty; not highlighted.

paper 0.7580 ±0.0100 Δ at pub 0.0002
84
GCN
actual #84 vs paper #88 4 places worse
0.7060 ±0.0369
best reported
actual #84 vs paper #88 4 places worse
paper 0.5000
paper 0.5000 Δ today 0.2060
85
WL
actual #85 vs paper #85
0.6882 ±0.0041
best reported
actual #85 vs paper #85
paper 0.6880 ±0.0040
best at pub: Graph Contrastive Learning Automated (ICML 2021)

Difference within reported uncertainty; not counted as underperformance.

paper 0.6880 ±0.0040 Δ at pub 0.0002 Δ today 0.0002
87
MLG
0.6330 ±0.0150
This paper
88
GCKN
0.5840 ±0.0760
This paper
SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Best today — OK at publication; today's leaderboard best is elsewhere