Graph Soft-Contrastive Learning via Neighborhood Ranking

Zhiyuan Ning, P. Wang, Pengyang Wang, Ziyue Qiao, Wei Fan, Denghui Zhang, Yi Du, Yuanchun Zhou

Main figure for Graph Soft-Contrastive Learning via Neighborhood Ranking

Abstract

Graph Contrastive Learning (GCL) has emerged as a promising approach in the realm of graph self-supervised learning. Prevailing GCL methods mainly derive from the principles of contrastive learning in the field of computer vision: modeling invariance by specifying absolutely similar pairs. However, when applied to graph data, this paradigm encounters two significant limitations: (1) the validity of the generated views cannot be guaranteed: graph perturbation may produce invalid views against semantics and intrinsic topology of graph data; (2) specifying absolutely similar pairs in the graph views is unreliable: for abstract and non-Euclidean graph data, it is difficult for humans to decide the absolute similarity and dissimilarity intuitively. Despite the notable performance of current GCL methods, these challenges necessitate a reevaluation: Could GCL be more effectively tailored to the intrinsic properties of graphs, rather than merely adopting principles from computer vision? In response to this query, we propose a novel paradigm, Graph Soft-Contrastive Learning (GSCL). This approach facilitates GCL via neighborhood ranking, avoiding the need to specify absolutely similar pairs. GSCL leverages the underlying graph characteristic of diminishing label consistency, asserting that nodes that are closer in the graph are overall more similar than far-distant nodes. Within the GSCL framework, we introduce pairwise and listwise gated ranking InfoNCE loss functions to effectively preserve the relative similarity ranking within neighborhoods. Moreover, as the neighborhood size exponentially expands with more hops considered, we propose neighborhood sampling strategies to improve learning efficiency. Our extensive empirical results across 11 commonly used graph datasets—including 8 homophily graphs and 3 heterophily graphs—demonstrate GSCL's superior performance compared to 20 state-of-the-art GCL methods.

Benchmark Results

Tested on 4 datasets 13 baseline values reported too low

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

Classic

#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT
actual #2 vs paper #275 273 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #275 273 places worse
paper 0.9256 ±0.0035
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN
actual #8 vs paper #292 284 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #292 284 places worse
paper 0.9242 ±0.0022
130
AFGRL
actual #130 vs paper #189 59 places worse
0.9361 ±0.0020
best reported
actual #130 vs paper #189 59 places worse
paper 0.9322 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.9322 ±0.0028 Δ at pub 0.0039
153
AutoSSL
actual #153 vs paper #254 101 places worse
0.9350 ±0.0070
best reported
actual #153 vs paper #254 101 places worse
paper 0.9271 ±0.0032

Difference within reported uncertainty; not counted as underperformance.

paper 0.9271 ±0.0032 Δ today 0.0079
162
GSCL-Pairwise
0.9342 ±0.0044
This paper
164
GraphMAE
actual #164 vs paper #415 251 places worse
0.9341 ±0.0010
best reported
actual #164 vs paper #415 251 places worse
paper 0.9071 ±0.0040
paper 0.9071 ±0.0040 Δ today 0.0270
170
GSCL-Listwise
0.9340 ±0.0048
This paper
172
BGRL
actual #172 vs paper #214 42 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #214 42 places worse
paper 0.9307 ±0.0034

Difference within reported uncertainty; not counted as underperformance.

paper 0.9307 ±0.0034 Δ at pub 0.0030
186
CCA-SSG
actual #186 vs paper #201 15 places worse
0.9325 ±0.0021
best reported
actual #186 vs paper #201 15 places worse
paper 0.9314 ±0.0014

Difference within reported uncertainty; not counted as underperformance.

paper 0.9314 ±0.0014 Δ at pub 0.0011
191
GCA
actual #191 vs paper #283 92 places worse
0.9320 ±0.0060
best reported
actual #191 vs paper #283 92 places worse
paper 0.9249 ±0.0009
paper 0.9249 ±0.0009 Δ at pub 0.0064 Δ today 0.0071
194
SUGRL
actual #194 vs paper #233 39 places worse
0.9285 ±0.0024
actual #194 vs paper #233 39 places worse
paper 0.9285 ±0.0024
203
GRACE
actual #203 vs paper #324 121 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #324 121 places worse
paper 0.9215 ±0.0024
paper 0.9215 ±0.0024 Δ at pub 0.0065 Δ today 0.0098
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
263
COSTA
actual #263 vs paper #275 12 places worse
0.9267 ±0.0016
best reported
actual #263 vs paper #275 12 places worse
paper 0.9256 ±0.0045

Difference within reported uncertainty; not counted as underperformance.

paper 0.9256 ±0.0045 Δ today 0.0011
267
G-BT
0.9263 ±0.0044
This paper
284
AF-GCL
0.9249 ±0.0031
This paper
317
VGAE
actual #317 vs paper #324 7 places worse
0.9224
best reported
actual #317 vs paper #324 7 places worse
paper 0.9220 ±0.0011

Difference within reported uncertainty; not counted as underperformance.

paper 0.9220 ±0.0011 Δ at pub 0.0004
352
GAE
actual #352 vs paper #366 14 places worse
0.9185 ±0.0006
best reported
actual #352 vs paper #366 14 places worse
paper 0.9162 ±0.0013
paper 0.9162 ±0.0013 Δ at pub 0.0023
390
MLP
0.9128 ±0.0063
408
GMI
actual #408 vs paper #417 9 places worse
0.9081 ±0.0015
best reported
actual #408 vs paper #417 9 places worse
paper 0.9068 ±0.0017

Difference within reported uncertainty; not counted as underperformance.

paper 0.9068 ±0.0017 Δ at pub 0.0002 Δ today 0.0013
444
DeepWalk
actual #444 vs paper #464 20 places worse
0.9005 ±0.0008
best reported
actual #444 vs paper #464 20 places worse
paper 0.8944 ±0.0011
paper 0.8944 ±0.0011 Δ at pub 0.0061 Δ today 0.0061
457
Node2Vec
actual #457 vs paper #458 1 place worse
0.8970 ±0.0010
best reported
actual #457 vs paper #458 1 place worse
paper 0.8967 ±0.0012

Difference within reported uncertainty; not counted as underperformance.

paper 0.8967 ±0.0012 Δ at pub 0.0003 Δ today 0.0003
531
Raw features
actual #531 vs paper #535 4 places worse
0.7999 ±0.0090
best reported
actual #531 vs paper #535 4 places worse
paper 0.7853
paper 0.7853 Δ today 0.0146
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN
actual #2 vs paper #269 267 places worse
0.9412 ±0.0008
best reported
actual #2 vs paper #269 267 places worse
paper 0.8651 ±0.0054
paper 0.8651 ±0.0054 Δ at pub 0.0134 Δ today 0.0761
3
GAT
actual #3 vs paper #256 253 places worse
0.9398 ±0.0022
best reported
actual #3 vs paper #256 253 places worse
paper 0.8693 ±0.0029
8
SAGE
0.9351 ±0.0006
79
BGRL
actual #79 vs paper #129 50 places worse
0.9034 ±0.0019
best reported
actual #79 vs paper #129 50 places worse
paper 0.8962 ±0.0037
paper 0.8962 ±0.0037 Δ at pub 0.0068 Δ today 0.0072
89
GSCL-Pairwise
0.9014 ±0.0035
This paper
100
GraphMAE
actual #100 vs paper #432 332 places worse
0.9002 ±0.0024
best reported
actual #100 vs paper #432 332 places worse
paper 0.7944 ±0.0048
paper 0.7944 ±0.0048 Δ at pub 0.0172 Δ today 0.1058
103
GSCL-Listwise
0.8999 ±0.0038
This paper
112
AFGRL
0.8988 ±0.0033
This paper
127
AF-GCL
0.8968 ±0.0019
This paper
139
GRACE
actual #139 vs paper #282 143 places worse
0.8953 ±0.0035
best reported
actual #139 vs paper #282 143 places worse
paper 0.8625 ±0.0025
paper 0.8625 ±0.0025 Δ at pub 0.0325 Δ today 0.0328
159
CCA-SSG
actual #159 vs paper #171 12 places worse
0.8874 ±0.0028
actual #159 vs paper #171 12 places worse
paper 0.8874 ±0.0028
paper 0.8874 ±0.0028 Δ at pub 0.0059
160
GCA
actual #160 vs paper #213 53 places worse
0.8894 ±0.0015
best reported
actual #160 vs paper #213 53 places worse
paper 0.8785 ±0.0031
paper 0.8785 ±0.0031 Δ at pub 0.0109 Δ today 0.0109
162
SUGRL
actual #162 vs paper #162
0.8893 ±0.0021
best reported
actual #162 vs paper #162
paper 0.8891 ±0.0022

Difference within reported uncertainty; not counted as underperformance.

paper 0.8891 ±0.0022 Δ today 0.0002
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
188
AutoSSL
actual #188 vs paper #200 12 places worse
0.8840 ±0.0030
best reported
actual #188 vs paper #200 12 places worse
paper 0.8818 ±0.0043

Difference within reported uncertainty; not counted as underperformance.

paper 0.8818 ±0.0043 Δ today 0.0022
192
COSTA
actual #192 vs paper #193 1 place worse
0.8837 ±0.0022
best reported
actual #192 vs paper #193 1 place worse
paper 0.8832 ±0.0003

Difference within reported uncertainty; not counted as underperformance.

paper 0.8832 ±0.0003 Δ today 0.0005
202
G-BT
0.8814 ±0.0033
This paper
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
paper 0.8395 ±0.0047 Δ at pub 0.0005 Δ today 0.0403
246
VGAE
actual #246 vs paper #274 28 places worse
0.8721 ±0.0026
best reported
actual #246 vs paper #274 28 places worse
paper 0.8637 ±0.0021
paper 0.8637 ±0.0021 Δ at pub 0.0007 Δ today 0.0084
264
GAE
actual #264 vs paper #305 41 places worse
0.8666 ±0.0007
best reported
actual #264 vs paper #305 41 places worse
paper 0.8527 ±0.0019
paper 0.8527 ±0.0019 Δ at pub 0.0139
278
DeepWalk
actual #278 vs paper #296 18 places worse
0.8628 ±0.0007
best reported
actual #278 vs paper #296 18 places worse
paper 0.8568 ±0.0006
paper 0.8568 ±0.0006 Δ at pub 0.0060 Δ today 0.0060
320
MLP
0.8463
330
Node2Vec
actual #330 vs paper #334 4 places worse
0.8440 ±0.0010
best reported
actual #330 vs paper #334 4 places worse
paper 0.8439 ±0.0008

Difference within reported uncertainty; not counted as underperformance.

paper 0.8439 ±0.0008 Δ today 0.0001
342
GMI
actual #342 vs paper #398 56 places worse
0.8422 ±0.0052
best reported
actual #342 vs paper #398 56 places worse
paper 0.8221 ±0.0031
paper 0.8221 ±0.0031 Δ today 0.0201
456
Raw features
0.7381
This paper
#ModelAccuracy ↑Paper
1
GCN
actual #1 vs paper #202 201 places worse
0.9302 ±0.0011
best reported
actual #1 vs paper #202 201 places worse
paper 0.7719 ±0.0012
paper 0.7719 ±0.0012 Δ at pub 0.1583
2
RSE + RGCN (70b)
0.8852 ±0.0019
3
LEMP+T
0.8825
9
SAGE
0.8771
31
GAT
actual #31 vs paper #187 156 places worse
0.8533
best reported
actual #31 vs paper #187 156 places worse
paper 0.7765 ±0.0011
84
GraphMAE
actual #84 vs paper #205 121 places worse
0.8052 ±0.0032
best reported
actual #84 vs paper #205 121 places worse
paper 0.7712 ±0.0030
paper 0.7712 ±0.0030 Δ today 0.0340
92
GSCL-Listwise
0.8016 ±0.0058
This paper
95
GSCL-Pairwise
0.8014 ±0.0051
This paper
94
GRACE
actual #94 vs paper #171 77 places worse
0.8014 ±0.0048
best reported
actual #94 vs paper #171 77 places worse
paper 0.7819 ±0.0001
paper 0.7819 ±0.0001 Δ at pub 0.0195 Δ today 0.0195
100
BGRL
actual #100 vs paper #117 17 places worse
0.8000 ±0.0010
best reported
actual #100 vs paper #117 17 places worse
paper 0.7931 ±0.0055

Difference within reported uncertainty; not counted as underperformance.

paper 0.7931 ±0.0055 Δ at pub 0.0069 Δ today 0.0069
129
COSTA
0.7912 ±0.0002
This paper
130
CCA-SSG
actual #130 vs paper #150 20 places worse
0.7865 ±0.0014
actual #130 vs paper #150 20 places worse
paper 0.7865 ±0.0014
paper 0.7865 ±0.0014 Δ at pub 0.0077
133
AF-GCL
0.7901 ±0.0051
This paper
138
SUGRL
0.7897 ±0.0022
This paper
143
AFGRL
actual #143 vs paper #187 44 places worse
0.7890 ±0.0060
best reported
actual #143 vs paper #187 44 places worse
paper 0.7762 ±0.0049
paper 0.7762 ±0.0049 Δ today 0.0128
151
DGI
actual #151 vs paper #228 77 places worse
0.7865 ±0.0690
best reported
actual #151 vs paper #228 77 places worse
paper 0.7535 ±0.0014

Difference within reported uncertainty; not counted as underperformance.

paper 0.7535 ±0.0014 Δ at pub 0.0005 Δ today 0.0330
162
GCA
actual #162 vs paper #166 4 places worse
0.7840 ±0.0013
best reported
actual #162 vs paper #166 4 places worse
paper 0.7830

Difference within reported uncertainty; not counted as underperformance.

paper 0.7830 Δ at pub 0.0010 Δ today 0.0010
181
GAE
actual #181 vs paper #265 84 places worse
0.7787 ±0.0053
best reported
actual #181 vs paper #265 84 places worse
paper 0.7015 ±0.0001
paper 0.7015 ±0.0001 Δ at pub 0.0382 Δ today 0.0772
180
VGAE
actual #180 vs paper #222 42 places worse
0.7787 ±0.0053
best reported
actual #180 vs paper #222 42 places worse
paper 0.7563 ±0.0019
190
MVGRL
actual #190 vs paper #191 1 place worse
0.7757 ±0.0046
best reported
actual #190 vs paper #191 1 place worse
paper 0.7752 ±0.0008

Difference within reported uncertainty; not counted as underperformance.

paper 0.7752 ±0.0008 Δ today 0.0005
198
DeepWalk
actual #198 vs paper #240 42 places worse
0.7721
best reported
actual #198 vs paper #240 42 places worse
paper 0.7435 ±0.0006
paper 0.7435 ±0.0006 Δ at pub 0.0286
211
G-BT
actual #211 vs paper #212 1 place worse
0.7683 ±0.0073
best reported
actual #211 vs paper #212 1 place worse
paper 0.7665 ±0.0062

Difference within reported uncertainty; not counted as underperformance.

paper 0.7665 ±0.0062 Δ today 0.0018
212
AutoSSL
0.7680 ±0.0013
This paper
234
GMI
actual #234 vs paper #234
0.7490 ±0.0010
best reported
actual #234 vs paper #234
paper 0.7485 ±0.0008

Difference within reported uncertainty; not counted as underperformance.

paper 0.7485 ±0.0008 Δ at pub 0.0005
237
MLP
0.7469 ±0.0085
256
Raw features
0.7198
This paper
258
Node2Vec
actual #258 vs paper #258
0.7180 ±0.0010
best reported
actual #258 vs paper #258
paper 0.7179 ±0.0005

Difference within reported uncertainty; not counted as underperformance.

paper 0.7179 ±0.0005 Δ at pub 0.0001

Heterophilic Graphs

#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
251
GRACE
actual #251 vs paper #390 139 places worse
0.3450 ±0.0110
best reported
actual #251 vs paper #390 139 places worse
paper 0.2827 ±0.0043
309
VGAE
actual #309 vs paper #385 76 places worse
0.3157 ±0.0075
best reported
actual #309 vs paper #385 76 places worse
paper 0.2843 ±0.0057
335
DGI
actual #335 vs paper #389 54 places worse
0.3067 ±0.0063
best reported
actual #335 vs paper #389 54 places worse
paper 0.2830 ±0.0076
341
GSCL-Pairwise
0.3032 ±0.0091
This paper
344
GSCL-Listwise
0.3023 ±0.0088
This paper
356
BGRL
actual #356 vs paper #377 21 places worse
0.2986
best reported
actual #356 vs paper #377 21 places worse
paper 0.2880 ±0.0054
361
GCA
actual #361 vs paper #376 15 places worse
0.2965
best reported
actual #361 vs paper #376 15 places worse
paper 0.2889 ±0.0050

Difference within reported uncertainty; not counted as underperformance.

paper 0.2889 ±0.0050 Δ today 0.0076
375
AF-GCL
0.2894 ±0.0069
This paper
383
GAE
actual #383 vs paper #429 46 places worse
0.2863 ±0.0105
best reported
actual #383 vs paper #429 46 places worse
paper 0.2536 ±0.0023
399
GMI
actual #399 vs paper #409 10 places worse
0.2782
best reported
actual #399 vs paper #409 10 places worse
paper 0.2728 ±0.0087

Difference within reported uncertainty; not counted as underperformance.

paper 0.2728 ±0.0087 Δ today 0.0054
407
AFGRL
0.2743 ±0.0131
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