Decoupled Self-supervised Learning for Non-Homophilou Graphs

Teng Xiao, Zhengyu Chen, Zhimeng Guo, Zeyang Zhuang, Suhang Wang

Main figure for Decoupled Self-supervised Learning for Non-Homophilou Graphs

Abstract

This paper studies the problem of conducting self-supervised learning for node representation learning on graphs. Most existing self-supervised learning methods assume the graph is homophilous, where linked nodes often belong to the same class or have similar features. However, such assumptions of homophily do not always hold in real-world graphs. We address this problem by developing a decoupled self-supervised learning (DSSL) framework for graph neural networks. DSSL imitates a generative process of nodes and links from latent variable modeling of the semantic structure, which decouples different underlying semantics between different neighborhoods into the self-supervised learning process. Our DSSL framework is agnostic to the encoders and does not need prefabricated augmentations, thus is flexible to different graphs. To effectively optimize the framework, we derive the evidence lower bound of the self-supervised objective and develop a scalable training algorithm with variational inference. We provide a theoretical analysis to justify that DSSL enjoys the better downstream performance. Extensive experiments on various types of graph benchmarks demonstrate that our proposed framework can achieve better performance compared with competitive baselines.

Proposed method: DSSL

Benchmark Results

Tested on 7 datasets 11 baseline values reported too low

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

Classic

#ModelAccuracy ↑Paper
1
GraphSAGE+CNA
0.9418 ±0.0033
2
GCN+CNA
0.9366 ±0.0048
3
TransformerConv
0.9350 ±0.0058
21
GCN
0.9004
156
MVGRL
actual #156 vs paper #220 64 places worse
0.8680 ±0.0050
best reported
actual #156 vs paper #220 64 places worse
paper 0.8521 ±0.0118

Difference within reported uncertainty; not counted as underperformance.

paper 0.8521 ±0.0118 Δ at pub 0.0017 Δ today 0.0159
177
DGI
actual #177 vs paper #288 111 places worse
0.8630 ±0.0020
best reported
actual #177 vs paper #288 111 places worse
paper 0.8417 ±0.0135
278
GraphCL
actual #278 vs paper #278
0.8428 ±0.0091
actual #278 vs paper #278
paper 0.8428 ±0.0091
423
DSSL
0.8306 ±0.0053
This paper
435
DeepWalk
actual #435 vs paper #738 303 places worse
0.8290
best reported
actual #435 vs paper #738 303 places worse
paper 0.7714 ±0.0082
paper 0.7714 ±0.0082 Δ at pub 0.0576
630
VGAE
actual #630 vs paper #630
0.8059 ±0.0035
actual #630 vs paper #630
paper 0.8059 ±0.0035
paper 0.8059 ±0.0035 Δ at pub 0.0328
654
GAE
actual #654 vs paper #709 55 places worse
0.8011 ±0.0022
best reported
actual #654 vs paper #709 55 places worse
paper 0.7833 ±0.0027
paper 0.7833 ±0.0027 Δ at pub 0.0178
697
LINE
actual #697 vs paper #697
0.7893 ±0.0055
actual #697 vs paper #697
paper 0.7893 ±0.0055
paper 0.7893 ±0.0055 Δ at pub 0.3573
724
MLP
0.7768
913
struc2vec
0.3026 ±0.0152
This paper
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
44
GCN
0.8033 ±0.0088
66
DGI
actual #66 vs paper #474 408 places worse
0.7890 ±0.0020
best reported
actual #66 vs paper #474 408 places worse
paper 0.7180 ±0.0133
87
MVGRL
actual #87 vs paper #445 358 places worse
0.7808 ±0.0006
best reported
actual #87 vs paper #445 358 places worse
paper 0.7213 ±0.0104
350
MLP
0.7289 ±0.0010
395
GraphCL
actual #395 vs paper #404 9 places worse
0.7246 ±0.0179
actual #395 vs paper #404 9 places worse
paper 0.7246 ±0.0179
prev best: Contrastive Laplacian Eigenmaps (NeurIPS 2022)

Improvement within reported uncertainty; not highlighted.

paper 0.7246 ±0.0179 Δ at pub 0.0136
625
VGAE
actual #625 vs paper #625
0.6990 ±0.0057
actual #625 vs paper #625
paper 0.6990 ±0.0057
paper 0.6990 ±0.0057 Δ at pub 0.0249
664
LINE
0.6879 ±0.0041
This paper
692
DeepWalk
actual #692 vs paper #692
0.6785 ±0.0079
actual #692 vs paper #692
paper 0.6785 ±0.0079
739
GAE
actual #739 vs paper #739
0.6639 ±0.0024
actual #739 vs paper #739
paper 0.6639 ±0.0024

Improvement within reported uncertainty; not highlighted.

paper 0.6639 ±0.0024 Δ at pub 0.0056
860
struc2vec
0.5338 ±0.0062
This paper
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
18
GCN
0.9296 ±0.0015
144
BGRL
actual #144 vs paper #353 209 places worse
0.8134 ±0.0050
actual #144 vs paper #353 209 places worse
paper 0.8134 ±0.0050
paper 0.8134 ±0.0050 Δ at pub 0.0116 Δ today 0.0696
196
MVGRL
actual #196 vs paper #320 124 places worse
0.8725 ±0.0012
best reported
actual #196 vs paper #320 124 places worse
paper 0.8233 ±0.0088
204
DGI
actual #204 vs paper #339 135 places worse
0.8708 ±0.0017
best reported
actual #204 vs paper #339 135 places worse
paper 0.8165 ±0.0071
210
MLP
0.8690 ±0.0074
223
DeepWalk
actual #223 vs paper #540 317 places worse
0.8652 ±0.0012
best reported
actual #223 vs paper #540 317 places worse
paper 0.7938 ±0.0122
299
VGAE
actual #299 vs paper #353 54 places worse
0.8133 ±0.0069
actual #299 vs paper #353 54 places worse
paper 0.8133 ±0.0069
303
DSSL
0.8298 ±0.0049
This paper
304
GAE
actual #304 vs paper #658 354 places worse
0.7828 ±0.0077
actual #304 vs paper #658 354 places worse
paper 0.7828 ±0.0077

Improvement within reported uncertainty; not highlighted.

paper 0.7828 ±0.0077 Δ at pub 0.0078 Δ today 0.0466
331
GraphCL
actual #331 vs paper #331
0.8196 ±0.0073
actual #331 vs paper #331
paper 0.8196 ±0.0073
401
LINE
0.8056 ±0.0092
This paper
881
struc2vec
0.4083 ±0.0185
This paper

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
304
DGI
actual #304 vs paper #532 228 places worse
0.5853 ±0.0298
actual #304 vs paper #532 228 places worse
paper 0.5853 ±0.0298

Improvement within reported uncertainty; not highlighted.

paper 0.5853 ±0.0298 Δ at pub 0.0443 Δ today 0.1728
351
MVGRL
actual #351 vs paper #575 224 places worse
0.7301 ±0.0552
best reported
actual #351 vs paper #575 224 places worse
paper 0.5342 ±0.0029
359
DSSL
actual #359 vs paper #477 118 places worse
0.7273 ±0.0402
best reported
actual #359 vs paper #477 118 places worse
paper 0.6211 ±0.0153
409
BGRL
actual #409 vs paper #576 167 places worse
0.6841 ±0.0501
best reported
actual #409 vs paper #576 167 places worse
paper 0.5277 ±0.0198
523
VGAE
actual #523 vs paper #580 57 places worse
0.5027 ±0.0221
actual #523 vs paper #580 57 places worse
paper 0.5027 ±0.0221

Improvement within reported uncertainty; not highlighted.

paper 0.5027 ±0.0221 Δ at pub 0.1109 Δ today 0.0893
526
GAE
actual #526 vs paper #574 48 places worse
0.5909 ±0.1626
best reported
actual #526 vs paper #574 48 places worse
paper 0.5398 ±0.0322

Difference within reported uncertainty; not counted as underperformance.

paper 0.5398 ±0.0322 Δ at pub 0.0480 Δ today 0.0511
585
struc2vec
actual #585 vs paper #585
0.4931 ±0.0322
actual #585 vs paper #585
paper 0.4931 ±0.0322

Improvement within reported uncertainty; not highlighted.

paper 0.4931 ±0.0322 Δ at pub 0.0202
588
LINE
0.4869 ±0.0139
This paper
589
GraphCL
actual #589 vs paper #589
0.4867 ±0.0437
actual #589 vs paper #589
paper 0.4867 ±0.0437

Improvement within reported uncertainty; not highlighted.

paper 0.4867 ±0.0437 Δ at pub 0.0219
595
DeepWalk
actual #595 vs paper #606 11 places worse
0.4231 ±0.0221
actual #595 vs paper #606 11 places worse
paper 0.4231 ±0.0221

Improvement within reported uncertainty; not highlighted.

paper 0.4231 ±0.0221 Δ at pub 0.0042
#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
289
DSSL
actual #289 vs paper #447 158 places worse
0.6928 ±0.0601
best reported
actual #289 vs paper #447 158 places worse
paper 0.5363 ±0.0116
340
MVGRL
actual #340 vs paper #475 135 places worse
0.6430
best reported
actual #340 vs paper #475 135 places worse
paper 0.5116 ±0.0167
350
DGI
actual #350 vs paper #524 174 places worse
0.6335
best reported
actual #350 vs paper #524 174 places worse
paper 0.4533 ±0.0611
354
GAE
actual #354 vs paper #533 179 places worse
0.6309 ±0.0987
best reported
actual #354 vs paper #533 179 places worse
paper 0.4418 ±0.0356
paper 0.4418 ±0.0356 Δ at pub 0.0122 Δ today 0.1891
386
VGAE
actual #386 vs paper #499 113 places worse
0.5919
best reported
actual #386 vs paper #499 113 places worse
paper 0.4873 ±0.0419
415
BGRL
actual #415 vs paper #485 70 places worse
0.5730
best reported
actual #415 vs paper #485 70 places worse
paper 0.5033 ±0.0229
500
DeepWalk
actual #500 vs paper #548 48 places worse
0.4155 ±0.0312
actual #500 vs paper #548 48 places worse
paper 0.4155 ±0.0312

Improvement within reported uncertainty; not highlighted.

paper 0.4155 ±0.0312 Δ at pub 0.0034
513
GraphCL
actual #513 vs paper #513
0.4722 ±0.0450
actual #513 vs paper #513
paper 0.4722 ±0.0450

Improvement within reported uncertainty; not highlighted.

paper 0.4722 ±0.0450 Δ at pub 0.0236
538
LINE
0.4368 ±0.0217
This paper
571
struc2vec
actual #571 vs paper #571
0.3022 ±0.0587
actual #571 vs paper #571
paper 0.3022 ±0.0587

Improvement within reported uncertainty; not highlighted.

paper 0.3022 ±0.0587 Δ at pub 0.0650
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
46
GCN
0.6067
50
MVGRL
actual #50 vs paper #178 128 places worse
0.6009 ±0.0044
best reported
actual #50 vs paper #178 128 places worse
paper 0.3843 ±0.0087
paper 0.3843 ±0.0087 Δ at pub 0.0032 Δ today 0.2166
108
BGRL
actual #108 vs paper #203 95 places worse
0.4624 ±0.0070
best reported
actual #108 vs paper #203 95 places worse
paper 0.3622 ±0.0197
141
VGAE
actual #141 vs paper #242 101 places worse
0.4250 ±0.0135
best reported
actual #141 vs paper #242 101 places worse
paper 0.2913 ±0.0116
paper 0.2913 ±0.0116 Δ at pub 0.0598 Δ today 0.1337
144
DGI
actual #144 vs paper #255 111 places worse
0.4222 ±0.0063
best reported
actual #144 vs paper #255 111 places worse
paper 0.2644 ±0.0112
160
DSSL
0.4051 ±0.0038
This paper
172
MLP
0.3930 ±0.0079
174
LINE
0.3892 ±0.0158
This paper
193
DeepWalk
actual #193 vs paper #193
0.3754 ±0.0219
actual #193 vs paper #193
paper 0.3754 ±0.0219
paper 0.3754 ±0.0219 Δ at pub 0.0664
202
struc2vec
0.3649 ±0.0115
This paper
225
GAE
actual #225 vs paper #240 15 places worse
0.3465 ±0.0081
best reported
actual #225 vs paper #240 15 places worse
paper 0.3053 ±0.0133
paper 0.3053 ±0.0133 Δ at pub 0.0412
274
GraphCL
0.2253 ±0.0098
This paper

LINKX Benchmarks

#ModelAccuracy ↑Paper
1
DC-GNN
0.8669 ±0.0022
2
M2M-GNN
0.8594 ±0.0040
3
GloGNN
0.8574 ±0.0042
29
GIN
0.8268 ±0.0032
51
MLP
0.7534 ±0.0064
68
BGRL
actual #68 vs paper #70 2 places worse
0.6331 ±0.0049
best reported
actual #68 vs paper #70 2 places worse
paper 0.5898 ±0.0013
paper 0.5898 ±0.0013 Δ today 0.0433
69
DSSL
0.6038 ±0.0032
This paper
71
GraphCL
0.5843 ±0.0031
This paper
72
VGAE
0.5829 ±0.0021
This paper
73
GAE
0.5811 ±0.0018
This paper
74
LINE
0.5759 ±0.0017
This paper
75
MVGRL
0.5722 ±0.0017
This paper
76
DeepWalk
0.5613 ±0.0046
This paper
77
DGI
0.5368 ±0.0019
This paper
78
struc2vec
0.5029 ±0.0031
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 Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere