Rethinking Semi-Supervised Node Classification with Self-Supervised Graph Clustering

Songbo Wang, Renchi Yang, Yurui Lai, Xiaoyang Lin, Tsz Nam Chan

Main figure for Rethinking Semi-Supervised Node Classification with Self-Supervised Graph Clustering

Abstract

The emergence of graph neural networks (GNNs) has offered a powerful tool for semi-supervised node classification tasks. Subsequent studies have achieved further improvements through refining the message passing schemes in GNN models or exploiting various data augmentation techniques to mitigate limited supervision. In real graphs, nodes often tend to form tightly-knit communities/clusters, which embody abundant signals for compensating label scarcity in semi-supervised node classification but are not explored in prior methods. Inspired by this, this paper presents NCGC that integrates self-supervised graph clustering and semi-supervised classification into a unified framework. Firstly, we theoretically unify the optimization objectives of GNNs and spectral graph clustering, and based on that, develop soft orthogonal GNNs (SOGNs) that leverage a refined message passing paradigm to generate node representations for both classification and clustering. On top of that, NCGC includes a self-supervised graph clustering module that enables the training of SOGNs for learning representations of unlabeled nodes in a self-supervised manner. Particularly, this component comprises two non-trivial clustering objectives and a Sinkhorn-Knopp normalization that transforms predicted cluster assignments into balanced soft pseudo-labels. Through combining the foregoing clustering module with the classification model using a multi-task objective containing the supervised classification loss on labeled data and self-supervised clustering loss on unlabeled data, NCGC promotes synergy between them and achieves enhanced model capacity. Our extensive experiments showcase that the proposed NCGC framework consistently and considerably outperforms popular GNN models and recent baselines for semi-supervised node classification on seven real graphs, when working with various classic GNN backbones.

Benchmark Results

Tested on 5 datasets 47 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*
actual #21 vs paper #245 224 places worse
0.9004
best reported
actual #21 vs paper #245 224 places worse
paper 0.8460 ±0.0066
paper 0.8460 ±0.0066 Δ at pub 0.0544
39
SAGE
0.8911 ±0.0012
44
GAT*
actual #44 vs paper #314 270 places worse
0.8897 ±0.0014
best reported
actual #44 vs paper #314 270 places worse
paper 0.8382 ±0.0085
45
GCNII
actual #45 vs paper #720 675 places worse
0.8893 ±0.0137
best reported
actual #45 vs paper #720 675 places worse
paper 0.7779 ±0.0197
best at pub: Language is All a Graph Needs (2023)
paper 0.7779 ±0.0197 Δ at pub 0.1114 Δ today 0.1114
55
JKNet
actual #55 vs paper #628 573 places worse
0.8870
best reported
actual #55 vs paper #628 573 places worse
paper 0.8063 ±0.0017
paper 0.8063 ±0.0017 Δ at pub 0.0807
70
DAGNN
actual #70 vs paper #642 572 places worse
0.8840
best reported
actual #70 vs paper #642 572 places worse
paper 0.8038 ±0.0173
paper 0.8038 ±0.0173 Δ at pub 0.0802
87
GRAND
actual #87 vs paper #572 485 places worse
0.8815
best reported
actual #87 vs paper #572 485 places worse
paper 0.8155 ±0.0027
paper 0.8155 ±0.0027 Δ at pub 0.0660
108
APPNP
actual #108 vs paper #642 534 places worse
0.8787
best reported
actual #108 vs paper #642 534 places worse
paper 0.8036 ±0.0301
best at pub: Orthogonal Graph Neural Networks (AAAI 2021)
paper 0.8036 ±0.0301 Δ at pub 0.0751 Δ today 0.0751
141
GraphSAGE*
actual #141 vs paper #377 236 places worse
0.8708 ±0.0085
best reported
actual #141 vs paper #377 236 places worse
paper 0.8346 ±0.0072
paper 0.8346 ±0.0072 Δ at pub 0.0362
162
GPR-GNN
actual #162 vs paper #572 410 places worse
0.8670 ±0.0103
best reported
actual #162 vs paper #572 410 places worse
paper 0.8151 ±0.0127
paper 0.8151 ±0.0127 Δ at pub 0.0519
174
NCGC (GCNII)
0.8640 ±0.0020
This paper
186
NormProp
0.8607
This paper
223
SGC
actual #223 vs paper #656 433 places worse
0.8509 ±0.0648
best reported
actual #223 vs paper #656 433 places worse
paper 0.8000 ±0.0107

Difference within reported uncertainty; not counted as underperformance.

paper 0.8000 ±0.0107 Δ at pub 0.0509
227
DND-Net
0.8498 ±0.0056
This paper
257
Violin
0.8449 ±0.0066
This paper
307
GraphMix
actual #307 vs paper #674 367 places worse
0.8394 ±0.0057
best reported
actual #307 vs paper #674 367 places worse
paper 0.7956 ±0.0086
paper 0.7956 ±0.0086 Δ at pub 0.0438
486
Meta-PN
0.8233 ±0.0079
This paper
501
GAM
actual #501 vs paper #764 263 places worse
0.8228 ±0.0048
best reported
actual #501 vs paper #764 263 places worse
paper 0.7566 ±0.0015
paper 0.7566 ±0.0015 Δ at pub 0.0662
526
PTA
0.8203 ±0.0105
This paper
587
MGCN
actual #587 vs paper #587
0.8123 ±0.0043
actual #587 vs paper #587
paper 0.8123 ±0.0043

Improvement within reported uncertainty; not highlighted.

paper 0.8123 ±0.0043 Δ at pub 0.0034
724
MLP
0.7768
735
M3S
0.7730 ±0.0046
This paper
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
17
APPNP
actual #17 vs paper #723 706 places worse
0.9355 ±0.0060
best reported
actual #17 vs paper #723 706 places worse
paper 0.7729 ±0.0082
paper 0.7729 ±0.0082 Δ at pub 0.1626
18
GCN*
actual #18 vs paper #402 384 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #402 384 places worse
paper 0.8052 ±0.0116
20
GAT*
actual #20 vs paper #582 562 places worse
0.9233 ±0.0018
best reported
actual #20 vs paper #582 562 places worse
paper 0.7906 ±0.0208
24
JKNet
actual #24 vs paper #794 770 places worse
0.9160
best reported
actual #24 vs paper #794 770 places worse
paper 0.7522 ±0.0084
paper 0.7522 ±0.0084 Δ at pub 0.1638
58
GCNII
actual #58 vs paper #764 706 places worse
0.9030 ±0.0043
best reported
actual #58 vs paper #764 706 places worse
paper 0.7618 ±0.0178
109
GRAND
actual #109 vs paper #789 680 places worse
0.8902
best reported
actual #109 vs paper #789 680 places worse
paper 0.7541 ±0.0051
paper 0.7541 ±0.0051 Δ at pub 0.1361
116
SAGE
0.8881 ±0.0015
125
GraphSAGE
actual #125 vs paper #519 394 places worse
0.8864 ±0.0030
best reported
actual #125 vs paper #519 394 places worse
paper 0.7947 ±0.0031
paper 0.7947 ±0.0031 Δ at pub 0.0917
141
SGC
actual #141 vs paper #763 622 places worse
0.8832 ±0.0055
best reported
actual #141 vs paper #763 622 places worse
paper 0.7623 ±0.0005
paper 0.7623 ±0.0005 Δ at pub 0.1209
191
GPR-GNN
actual #191 vs paper #652 461 places worse
0.8738 ±0.0063
best reported
actual #191 vs paper #652 461 places worse
paper 0.7830 ±0.0161
paper 0.7830 ±0.0161 Δ at pub 0.0908
210
MLP
0.8690 ±0.0074
226
DAGNN
actual #226 vs paper #711 485 places worse
0.8640
best reported
actual #226 vs paper #711 485 places worse
paper 0.7750 ±0.0131
paper 0.7750 ±0.0131 Δ at pub 0.0890
329
NCGC (GCNII)
0.8203 ±0.0032
This paper
333
Meta-PN
0.8190 ±0.0045
This paper
343
NormProp
0.8153 ±0.0001
This paper
359
Violin
0.8123 ±0.0042
This paper
367
GraphMix
actual #367 vs paper #645 278 places worse
0.8110 ±0.0078
best reported
actual #367 vs paper #645 278 places worse
paper 0.7847 ±0.0134
paper 0.7847 ±0.0134 Δ at pub 0.0263
382
PTA
0.8087 ±0.0062
This paper
497
GAM
actual #497 vs paper #659 162 places worse
0.7960 ±0.0063
best reported
actual #497 vs paper #659 162 places worse
paper 0.7825 ±0.0025
paper 0.7825 ±0.0025 Δ at pub 0.0135
510
M3S
actual #510 vs paper #784 274 places worse
0.7950 ±0.0076
best reported
actual #510 vs paper #784 274 places worse
paper 0.7558 ±0.0115
paper 0.7558 ±0.0115 Δ at pub 0.0392
660
DND-Net
0.7824 ±0.0098
This paper
761
MGCN
0.7634 ±0.0073
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9703 ±0.0019
2
GAT*
actual #2 vs paper #377 375 places worse
0.9669 ±0.0014
best reported
actual #2 vs paper #377 375 places worse
paper 0.9143 ±0.0015
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
8
GCN*
actual #8 vs paper #438 430 places worse
0.9632 ±0.0008
best reported
actual #8 vs paper #438 430 places worse
paper 0.9034 ±0.0084
20
GRAND
actual #20 vs paper #523 503 places worse
0.9579 ±0.0059
best reported
actual #20 vs paper #523 503 places worse
paper 0.8275 ±0.0038
best at pub: Graph Wave Networks (WWW 2025)
paper 0.8275 ±0.0038 Δ at pub 0.1304
21
APPNP
actual #21 vs paper #497 476 places worse
0.9573 ±0.0012
best reported
actual #21 vs paper #497 476 places worse
paper 0.8698 ±0.0020
paper 0.8698 ±0.0020 Δ at pub 0.0875
50
SGC
actual #50 vs paper #511 461 places worse
0.9511 ±0.0009
best reported
actual #50 vs paper #511 461 places worse
paper 0.8451 ±0.0040
paper 0.8451 ±0.0040 Δ at pub 0.1060
56
GraphSAGE*
actual #56 vs paper #399 343 places worse
0.9508 ±0.0026
best reported
actual #56 vs paper #399 343 places worse
paper 0.9115 ±0.0055
paper 0.9115 ±0.0055 Δ at pub 0.0393
87
GCNII
actual #87 vs paper #491 404 places worse
0.9430 ±0.0020
best reported
actual #87 vs paper #491 404 places worse
paper 0.8778 ±0.0148
paper 0.8778 ±0.0148 Δ at pub 0.0652
112
GPR-GNN
actual #112 vs paper #407 295 places worse
0.9385 ±0.0028
best reported
actual #112 vs paper #407 295 places worse
paper 0.9081 ±0.0018
paper 0.9081 ±0.0018 Δ at pub 0.0304
253
NCGC (GAT)
0.9274 ±0.0038
This paper
260
DAGNN
actual #260 vs paper #412 152 places worse
0.9269
best reported
actual #260 vs paper #412 152 places worse
paper 0.9078 ±0.0022
paper 0.9078 ±0.0022 Δ at pub 0.0191
266
MGCN
actual #266 vs paper #424 158 places worse
0.9264 ±0.0024
best reported
actual #266 vs paper #424 158 places worse
paper 0.9056 ±0.0062
paper 0.9056 ±0.0062 Δ at pub 0.0208
346
NormProp
0.9193 ±0.0044
This paper
364
JKNet
actual #364 vs paper #455 91 places worse
0.9169
best reported
actual #364 vs paper #455 91 places worse
paper 0.8976 ±0.0012
paper 0.8976 ±0.0012 Δ at pub 0.0193
390
MLP
0.9128 ±0.0063
395
GAM
0.9123 ±0.0032
This paper
486
GraphMix
0.8845 ±0.0076
This paper
497
M3S
0.8709 ±0.0052
This paper
532
Meta-PN
0.7932 ±0.1271
This paper
551
PTA
0.7417 ±0.0157
This paper
#ModelAccuracy ↑Paper
1
GraphTARIF
0.9461 ±0.0017
2
GCN*
actual #2 vs paper #417 415 places worse
0.9412 ±0.0008
best reported
actual #2 vs paper #417 415 places worse
paper 0.8111 ±0.0160
3
GAT*
actual #3 vs paper #413 410 places worse
0.9398 ±0.0022
best reported
actual #3 vs paper #413 410 places worse
paper 0.8136 ±0.0143
8
SAGE
0.9351 ±0.0006
46
GraphSAGE*
actual #46 vs paper #401 355 places worse
0.9120 ±0.0029
best reported
actual #46 vs paper #401 355 places worse
paper 0.8210 ±0.0139
paper 0.8210 ±0.0139 Δ at pub 0.0910 Δ today 0.0910
52
GCNII
actual #52 vs paper #453 401 places worse
0.9104 ±0.0041
best reported
actual #52 vs paper #453 401 places worse
paper 0.7472 ±0.0503
paper 0.7472 ±0.0503 Δ at pub 0.1632
58
APPNP
actual #58 vs paper #462 404 places worse
0.9093 ±0.0018
best reported
actual #58 vs paper #462 404 places worse
paper 0.7311 ±0.0025
paper 0.7311 ±0.0025 Δ at pub 0.1782
82
SGC
actual #82 vs paper #463 381 places worse
0.9022 ±0.0021
best reported
actual #82 vs paper #463 381 places worse
paper 0.7284 ±0.0148
paper 0.7284 ±0.0148 Δ at pub 0.1738
144
GRAND
actual #144 vs paper #474 330 places worse
0.8937 ±0.0041
best reported
actual #144 vs paper #474 330 places worse
paper 0.6976 ±0.0052
best at pub: Graph Wave Networks (WWW 2025)
paper 0.6976 ±0.0052 Δ at pub 0.1961
230
JKNet
actual #230 vs paper #427 197 places worse
0.8760
best reported
actual #230 vs paper #427 197 places worse
paper 0.8045 ±0.0053
paper 0.8045 ±0.0053 Δ at pub 0.0715
320
MLP
0.8463
324
DAGNN
actual #324 vs paper #420 96 places worse
0.8450 ±0.0120
best reported
actual #324 vs paper #420 96 places worse
paper 0.8081 ±0.0093
paper 0.8081 ±0.0093 Δ at pub 0.0369
350
NCGC (GAT)
0.8401 ±0.0094
This paper
353
MGCN
actual #353 vs paper #487 134 places worse
0.8399 ±0.0090
best reported
actual #353 vs paper #487 134 places worse
paper 0.5477 ±0.0234
paper 0.5477 ±0.0234 Δ at pub 0.2922
397
GPR-GNN
actual #397 vs paper #431 34 places worse
0.8238 ±0.0160
best reported
actual #397 vs paper #431 34 places worse
paper 0.7952 ±0.0200

Difference within reported uncertainty; not counted as underperformance.

paper 0.7952 ±0.0200 Δ at pub 0.0286
411
GAM
0.8164 ±0.0036
This paper
448
M3S
0.7592 ±0.0107
This paper
463
NormProp
0.7298 ±0.0464
This paper
465
Meta-PN
0.7246 ±0.0732
This paper
466
GraphMix
0.7154 ±0.0045
This paper
487
PTA
0.5541 ±0.0279
This paper
#ModelAccuracy ↑Paper
1
GrokFormer
0.9831 ±0.0018
2
PolyFormer
0.9808 ±0.0027
3
SGFormer
0.9796 ±0.0081
6
GAT
actual #6 vs paper #260 254 places worse
0.9782 ±0.0028
best reported
actual #6 vs paper #260 254 places worse
paper 0.9216 ±0.0060
paper 0.9216 ±0.0060 Δ at pub 0.0566
9
GCN*
actual #9 vs paper #245 236 places worse
0.9774 ±0.0035
best reported
actual #9 vs paper #245 236 places worse
paper 0.9283 ±0.0020
paper 0.9283 ±0.0020 Δ at pub 0.0491
17
SAGE
0.9739 ±0.0018
42
APPNP
actual #42 vs paper #215 173 places worse
0.9654 ±0.0007
best reported
actual #42 vs paper #215 173 places worse
paper 0.9353 ±0.0013
paper 0.9353 ±0.0013 Δ at pub 0.0301
43
GraphSAGE*
actual #43 vs paper #246 203 places worse
0.9649 ±0.0006
best reported
actual #43 vs paper #246 203 places worse
paper 0.9270 ±0.0046
paper 0.9270 ±0.0046 Δ at pub 0.0379
59
GCNII
actual #59 vs paper #246 187 places worse
0.9597 ±0.0011
best reported
actual #59 vs paper #246 187 places worse
paper 0.9275 ±0.0009
paper 0.9275 ±0.0009 Δ at pub 0.0322
58
MLP
0.9597 ±0.0007
70
SGC
actual #70 vs paper #267 197 places worse
0.9580 ±0.0010
best reported
actual #70 vs paper #267 197 places worse
paper 0.9132 ±0.0062
paper 0.9132 ±0.0062 Δ at pub 0.0448 Δ today 0.0448
177
GraphMix
actual #177 vs paper #255 78 places worse
0.9449 ±0.0084
best reported
actual #177 vs paper #255 78 places worse
paper 0.9245 ±0.0084
paper 0.9245 ±0.0084 Δ at pub 0.0204
179
NCGC (GCN)
0.9441 ±0.0029
This paper
188
NormProp
0.9428
This paper
189
PTA
0.9424 ±0.0031
This paper
197
DAGNN
actual #197 vs paper #219 22 places worse
0.9401 ±0.0060
best reported
actual #197 vs paper #219 22 places worse
paper 0.9339 ±0.0001

Difference within reported uncertainty; not counted as underperformance.

paper 0.9339 ±0.0001 Δ at pub 0.0062
215
GPR-GNN
0.9357 ±0.0011
This paper
221
GAM
0.9331 ±0.0151
This paper
227
JKNet
actual #227 vs paper #245 18 places worse
0.9325 ±0.0082
best reported
actual #227 vs paper #245 18 places worse
paper 0.9280 ±0.0025

Difference within reported uncertainty; not counted as underperformance.

paper 0.9280 ±0.0025 Δ at pub 0.0045
248
GRAND
0.9264 ±0.0012
This paper
262
Meta-PN
0.9206 ±0.0123
This paper
274
M3S
0.8945 ±0.0095
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)