Smoothed Graph Contrastive Learning via Seamless Proximity Integration

M. Behmanesh, M. Ovsjanikov

Main figure for Smoothed Graph Contrastive Learning via Seamless Proximity Integration

Abstract

Graph contrastive learning (GCL) aligns node representations by classifying node pairs into positives and negatives using a selection process that typically relies on establishing correspondences within two augmented graphs. The conventional GCL approaches incorporate negative samples uniformly in the contrastive loss, resulting in the equal treatment of negative nodes, regardless of their proximity to the true positive. In this paper, we present a Smoothed Graph Contrastive Learning model (SGCL), which leverages the geometric structure of augmented graphs to inject proximity information associated with positive/negative pairs in the contrastive loss, thus significantly regularizing the learning process. The proposed SGCL adjusts the penalties associated with node pairs in contrastive loss by incorporating three distinct smoothing techniques that result in proximity-aware positives and negatives. To enhance scalability for large-scale graphs, the proposed framework incorporates a graph batch-generating strategy that partitions the given graphs into multiple subgraphs, facilitating efficient training in separate batches. Through extensive experimentation in the unsupervised setting on various benchmarks, particularly those of large scale, we demonstrate the superiority of our proposed framework against recent baselines. The implementation is available at.

Benchmark Results

Tested on 12 datasets 4 baseline values reported too low Non-standard metric on 1 dataset

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

Classic

#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
0.9669 ±0.0014
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
123
SGCL-B
0.9372 ±0.0012
This paper
129
ProGCL-mix
0.9364 ±0.0013
This paper
132
GREET
actual #132 vs paper #233 101 places worse
0.9361 ±0.0035
best reported
actual #132 vs paper #233 101 places worse
paper 0.9285 ±0.0031
159
AUGCL
0.9343 ±0.0032
This paper
172
BGRL
actual #172 vs paper #198 26 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #198 26 places worse
paper 0.9317 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.9317 ±0.0030 Δ at pub 0.0020
180
ProGCL-weight
0.9330 ±0.0009
This paper
203
GRACE
actual #203 vs paper #244 41 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #244 41 places worse
paper 0.9278 ±0.0045

Difference within reported uncertainty; not counted as underperformance.

paper 0.9278 ±0.0045 Δ at pub 0.0002 Δ today 0.0035
204
SGCL-T
0.9312 ±0.0070
This paper
206
MVGRL
actual #206 vs paper #359 153 places worse
0.9310 ±0.0040
best reported
actual #206 vs paper #359 153 places worse
paper 0.9174 ±0.0007
213
DGI
actual #213 vs paper #366 153 places worse
0.9309 ±0.0008
best reported
actual #213 vs paper #366 153 places worse
paper 0.9161 ±0.0022
232
SGCL-D
0.9287 ±0.0060
This paper
267
G-BT
0.9263 ±0.0044
This paper
299
CGRA
0.9240 ±0.0020
This paper
311
GRLC
0.9230 ±0.0050
This paper
390
MLP
0.9128 ±0.0063
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
0.9412 ±0.0008
3
GAT
0.9398 ±0.0022
8
SAGE
0.9351 ±0.0006
74
CGRA
0.9050 ±0.0040
This paper
79
BGRL
0.9034 ±0.0019
This paper
119
SGCL-B
0.8975 ±0.0080
This paper
136
ProGCL-mix
0.8955 ±0.0016
This paper
139
GRACE
0.8953 ±0.0035
This paper
148
ProGCL-weight
0.8928 ±0.0015
This paper
161
AUGCL
0.8894 ±0.0044
This paper
179
MVGRL
actual #179 vs paper #235 56 places worse
0.8861 ±0.0064
best reported
actual #179 vs paper #235 56 places worse
paper 0.8752 ±0.0011
184
GRLC
0.8854 ±0.0023
This paper
202
G-BT
0.8814 ±0.0033
This paper
209
GREET
actual #209 vs paper #212 3 places worse
0.8802 ±0.0058
best reported
actual #209 vs paper #212 3 places worse
paper 0.8794 ±0.0035

Difference within reported uncertainty; not counted as underperformance.

paper 0.8794 ±0.0035 Δ today 0.0008
210
DGI
actual #210 vs paper #354 144 places worse
0.8798 ±0.0081
best reported
actual #210 vs paper #354 144 places worse
paper 0.8395 ±0.0047
247
SGCL-T
0.8721 ±0.0042
This paper
286
SGCL-D
0.8611 ±0.0030
This paper
320
MLP
0.8463
#ModelAccuracy ↑Paper
1
DoG
0.9690 ±0.0030
2
GWN-fa
0.9667 ±0.0026
3
GWN-sym
0.9666 ±0.0026
6
GraphSAGE
0.9593 ±0.0025
19
GREET
0.9465 ±0.0018
This paper
36
ProGCL-mix
0.9367 ±0.0012
This paper
42
ProGCL-weight
0.9351 ±0.0006
This paper
43
DGI
actual #43 vs paper #114 71 places worse
0.9350 ±0.0030
best reported
actual #43 vs paper #114 71 places worse
paper 0.9215 ±0.0063
53
BGRL
0.9331 ±0.0013
This paper
69
GRACE
actual #69 vs paper #148 79 places worse
0.9301 ±0.0003
best reported
actual #69 vs paper #148 79 places worse
paper 0.9112 ±0.0020
paper 0.9112 ±0.0020 Δ at pub 0.0181 Δ today 0.0189
77
G-BT
0.9295 ±0.0017
This paper
89
CGRA
0.9280 ±0.0050
This paper
88
MLP
0.9280 ±0.0020
107
SGCL-B
0.9233 ±0.0040
This paper
113
SGCL-T
0.9225 ±0.0015
This paper
115
SGCL-D
0.9214 ±0.0026
This paper
116
MVGRL
0.9211 ±0.0012
This paper
159
GRLC
0.9036 ±0.0027
This paper

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
108
CGRA
0.9110 ±0.0250
This paper
178
AD-GCL
actual #178 vs paper #396 218 places worse
0.9028 ±0.0401
best reported
actual #178 vs paper #396 218 places worse
paper 0.8680 ±0.0130

Difference within reported uncertainty; not counted as underperformance.

paper 0.8680 ±0.0130 Δ at pub 0.0348
180
LaGraph
0.9020 ±0.0110
This paper
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 at pub 0.0023
243
BGRL
actual #243 vs paper #421 178 places worse
0.8600 ±0.0180
actual #243 vs paper #421 178 places worse
paper 0.8600 ±0.0180

Improvement within reported uncertainty; not highlighted.

paper 0.8600 ±0.0180 Δ at pub 0.1101 Δ today 0.0340
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

Difference within reported uncertainty; not counted as underperformance.

paper 0.8900 ±0.0110 Δ at pub 0.0030
267
AUGCL
0.8920 ±0.0100
This paper
275
SGCL-T
0.8900 ±0.0230
This paper
298
ProGCL-mix
0.8870 ±0.0140
This paper
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

Difference within reported uncertainty; not counted as underperformance.

paper 0.8680 ±0.0130 Δ at pub 0.0086
396
SGCL-B
0.8700 ±0.0280
This paper
403
MLP
0.8660 ±0.0495
423
SGCL-D
0.8600 ±0.0260
This paper
#ModelAccuracy ↑Paper
1
GMN
0.7866
2
MemGNN
0.7550
3
TFGW SP
0.7510 ±0.0500
17
GatedGCN
0.7000 ±0.0494
26
GraphSAGE
0.6817 ±0.0545
47
SGCL-T
0.6530 ±0.0360
This paper
57
SGCL-D
0.6430 ±0.0220
This paper
60
SGCL-B
0.6370 ±0.0160
This paper
81
CGRA
0.6110 ±0.0090
This paper
124
MLP
0.5583 ±0.0352
131
GraphCL
actual #131 vs paper #131
0.5510 ±0.0160
actual #131 vs paper #131
paper 0.5510 ±0.0160
paper 0.5510 ±0.0160 Δ at pub 0.2227
155
BGRL
0.5070 ±0.0900
This paper
158
InfoGraph
actual #158 vs paper #158
0.5020 ±0.0140
actual #158 vs paper #158
paper 0.5020 ±0.0140
paper 0.5020 ±0.0140 Δ at pub 0.2347
162
MVGRL
actual #162 vs paper #162
0.4830 ±0.0120
actual #162 vs paper #162
paper 0.4830 ±0.0120
paper 0.4830 ±0.0120 Δ at pub 0.1410
180
AD-GCL
actual #180 vs paper #180
0.4260 ±0.0110
actual #180 vs paper #180
paper 0.4260 ±0.0110
paper 0.4260 ±0.0110 Δ at pub 0.1527
185
LaGraph
0.4090 ±0.0170
This paper
#ModelAccuracy ↑Paper
1
ID-GNN+BEC
0.8150 ±0.0240
2
GIN+BEC
0.8080 ±0.0330
3
GCN+BEC
0.7990 ±0.0340
4
GCN
0.7980 ±0.0230
28
SGCL-D
0.7580 ±0.0190
This paper
30
CGRA
0.7560 ±0.0050
This paper
35
SGCL-T
0.7520 ±0.0280
This paper
51
MVGRL
0.7420 ±0.0070
This paper
59
LaGraph
0.7370 ±0.0090
This paper
76
SGCL-B
0.7320 ±0.0370
This paper
82
InfoGraph
actual #82 vs paper #82
0.7303 ±0.0087
best reported
actual #82 vs paper #82
paper 0.7300 ±0.0090

Difference within reported uncertainty; not counted as underperformance.

paper 0.7300 ±0.0090 Δ at pub 0.0003 Δ today 0.0003
89
BGRL
0.7280 ±0.0050
This paper
97
AUGCL
0.7240 ±0.0080
This paper
116
ProGCL-mix
0.7160 ±0.0060
This paper
119
AD-GCL
actual #119 vs paper #119
0.7150 ±0.0100
actual #119 vs paper #119
paper 0.7150 ±0.0100

Improvement within reported uncertainty; not highlighted.

paper 0.7150 ±0.0100 Δ at pub 0.0030
124
GraphCL
actual #124 vs paper #124
0.7114 ±0.0044
best reported
actual #124 vs paper #124
paper 0.7110 ±0.0040

Difference within reported uncertainty; not counted as underperformance.

paper 0.7110 ±0.0040 Δ at pub 0.0004 Δ today 0.0004

OGB

#ModelAccuracy ↑Paper
1
Jacobi
0.8968
2
GPR
0.8953
3
LEMP4HG
0.8939
4
SAGE
0.8933
26
DGI
actual #26 vs paper #342 316 places worse
0.8637 ±0.0019
best reported
actual #26 vs paper #342 316 places worse
paper 0.6868 ±0.0060
paper 0.6868 ±0.0060 Δ at pub 0.1769
125
GraphMAE2
actual #125 vs paper #289 164 places worse
0.8108 ±0.0800
best reported
actual #125 vs paper #289 164 places worse
paper 0.7432 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.7432 ±0.0050 Δ today 0.0676
243
SGCL-T
0.7597 ±0.0010
This paper
289
SGCL-B
0.7433 ±0.0040
This paper
294
SGCL-D
0.7415 ±0.0020
This paper
300
BGRL
actual #300 vs paper #350 50 places worse
0.7397 ±0.0005
best reported
actual #300 vs paper #350 50 places worse
paper 0.6623 ±0.0050
paper 0.6623 ±0.0050 Δ at pub 0.0774
317
GRACE
actual #317 vs paper #317
0.7210 ±0.0070
actual #317 vs paper #317
paper 0.7210 ±0.0070
paper 0.7210 ±0.0070 Δ at pub 0.0400
337
MVGRL
0.6990 ±0.0090
This paper
351
MLP
0.6605 ±0.0020
353
GBT
0.6574 ±0.0040
This paper

ogbn-proteins

Global leaderboard →
Non-default metric. This paper reports Accuracy; the dataset default is ROC-AUC. Values below use Accuracy only.

Sorted by Accuracy. Highlighted rows are from other papers.

#ModelAccuracy ↑Paper
1
SGCL-T
0.9464 ±0.0020
This paper
2
DGI
0.9411 ±0.0010
This paper
3
GRACE
0.9411 ±0.0020
This paper
4
GBT
0.9407 ±0.0030
This paper
5
MVGRL
0.9387 ±0.0030
This paper
6
SGCL-B
0.9355 ±0.0020
This paper
7
SGCL-D
0.9319 ±0.0010
This paper
8
BGRL
0.9294 ±0.0030
This paper
11
GCN
0.7251 ±0.0031

Heterophilic Graphs

#ModelAccuracy ↑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
563
SGCL-D
0.5548 ±0.0270
This paper
571
SGCL-B
0.5497 ±0.0230
This paper
572
SGCL-T
0.5456 ±0.0180
This paper
576
GCL (GRACE)
0.5307 ±0.0240
This paper
#ModelAccuracy ↑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
426
SGCL-B
0.5579 ±0.0120
This paper
432
SGCL-T
0.5445 ±0.0060
This paper
454
SGCL-D
0.5312 ±0.0540
This paper
461
GCL (GRACE)
0.5221 ±0.0130
This paper
#ModelAccuracy ↑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
366
SGCL-T
0.2929 ±0.0047
This paper
369
SGCL-B
0.2915 ±0.0028
This paper
379
SGCL-D
0.2874 ±0.0076
This paper
385
GCL (GRACE)
0.2855 ±0.0028
This paper

LINKX Benchmarks

#ModelAccuracy ↑Paper
1
DGT
0.6609 ±0.0022
2
ICG_u-NN
0.6608 ±0.0074
3
LINKX
0.6606 ±0.0019
14
GraphSAGE
0.6473 ±0.0011
33
MLP
0.6114 ±0.0006
43
SGCL-B
0.5938 ±0.0088
This paper
44
SGCL-T
0.5937 ±0.0047
This paper
45
SGCL-D
0.5860 ±0.0048
This paper
46
GCL (GRACE)
0.5821 ±0.0051
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 at pub — reported value improved over the best known when published Best today — OK at publication; today's leaderboard best is elsewhere