Spectral-Aware Augmentation for Enhanced Graph Representation Learning

Kaiqi Yang, Haoyu Han, Wei Jin, Hui Liu

Main figure for Spectral-Aware Augmentation for Enhanced Graph Representation Learning

Abstract

Graph Contrastive Learning (GCL) has demonstrated remarkable effectiveness in learning representations on graphs in recent years. To generate ideal augmentation views, the augmentation generation methods should preserve essential information while discarding less relevant details for downstream tasks. However, current augmentation methods usually involve random topology corruption in the spatial domain, which fails to adequately address information spread across different frequencies in the spectral domain. Our preliminary study highlights this issue, demonstrating that spatial random perturbations impact all frequency bands almost uniformly. Given that task-relevant information typically resides in specific spectral regions that vary across graphs, this one-size-fits-all approach can pose challenges. We argue that indiscriminate spatial random perturbation might unintentionally weaken task-relevant information, reducing its effectiveness. To tackle this challenge, we propose applying perturbations selectively, focusing on information specific to different frequencies across diverse graphs. In this paper, we present GASSER, a model that applies tailored perturbations to specific frequencies of graph structures in the spectral domain, guided by spectral hints. Through extensive experimentation and theoretical analysis, we demonstrate that the augmentation views generated by GASSER are adaptive, controllable, and intuitively aligned with the homophily ratios and spectrum of graph structures.

Benchmark Results

Tested on 7 datasets 34 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 #572 551 places worse
0.9004
best reported
actual #21 vs paper #572 551 places worse
paper 0.8154 ±0.0068
paper 0.8154 ±0.0068 Δ at pub 0.0650 Δ today 0.0850
39
SAGE
0.8911 ±0.0012
130
BGRL
actual #130 vs paper #578 448 places worse
0.8730 ±0.0010
best reported
actual #130 vs paper #578 448 places worse
paper 0.8144 ±0.0072
paper 0.8144 ±0.0072 Δ at pub 0.0586
134
GRACE
actual #134 vs paper #536 402 places worse
0.8720 ±0.0020
best reported
actual #134 vs paper #536 402 places worse
paper 0.8190 ±0.0040
paper 0.8190 ±0.0040 Δ at pub 0.0530
156
MVGRL
actual #156 vs paper #438 282 places worse
0.8680 ±0.0050
best reported
actual #156 vs paper #438 282 places worse
paper 0.8289 ±0.0009
paper 0.8289 ±0.0009 Δ at pub 0.0391 Δ today 0.0391
177
DGI
actual #177 vs paper #486 309 places worse
0.8630 ±0.0020
best reported
actual #177 vs paper #486 309 places worse
paper 0.8230 ±0.0060
paper 0.8230 ±0.0060 Δ at pub 0.0400
216
GASSER
0.8527 ±0.0010
This paper
217
CCA-SSG+GASSER
0.8527 ±0.0010
This paper
248
CCA-SSG
actual #248 vs paper #278 30 places worse
0.8460 ±0.0070
best reported
actual #248 vs paper #278 30 places worse
paper 0.8420 ±0.0040

Difference within reported uncertainty; not counted as underperformance.

paper 0.8420 ±0.0040 Δ at pub 0.0040
293
GRACE+GASSER
0.8410 ±0.0026
This paper
394
GCL-SPAN
0.8330 ±0.0049
This paper
414
AF-GCL
0.8316 ±0.0013
This paper
415
GCA
actual #415 vs paper #523 108 places worse
0.8310 ±0.0030
best reported
actual #415 vs paper #523 108 places worse
paper 0.8207 ±0.0010
paper 0.8207 ±0.0010 Δ at pub 0.0103
643
MVGRL+GASSER
0.8036 ±0.0005
This paper
724
MLP
actual #724 vs paper #904 180 places worse
0.7768
best reported
actual #724 vs paper #904 180 places worse
paper 0.4792 ±0.0041
paper 0.4792 ±0.0041 Δ at pub 0.2683 Δ today 0.2976
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
44
GCN
actual #44 vs paper #576 532 places worse
0.8033 ±0.0088
best reported
actual #44 vs paper #576 532 places worse
paper 0.7073 ±0.0065
paper 0.7073 ±0.0065 Δ at pub 0.0870 Δ today 0.0960
61
GraphSAGE
0.7923 ±0.0053
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 ±0.0070
paper 0.7180 ±0.0070 Δ at pub 0.0710
87
MVGRL
actual #87 vs paper #292 205 places worse
0.7808 ±0.0006
best reported
actual #87 vs paper #292 205 places worse
paper 0.7330 ±0.0050
136
BGRL
actual #136 vs paper #474 338 places worse
0.7600 ±0.0020
best reported
actual #136 vs paper #474 338 places worse
paper 0.7182 ±0.0048
paper 0.7182 ±0.0048 Δ at pub 0.0418
163
GASSER
0.7541 ±0.0084
This paper
164
CCA-SSG+GASSER
0.7541 ±0.0084
This paper
165
CCA-SSG
actual #165 vs paper #316 151 places worse
0.7540 ±0.0100
best reported
actual #165 vs paper #316 151 places worse
paper 0.7310 ±0.0030
paper 0.7310 ±0.0030 Δ at pub 0.0230
201
GRACE
actual #201 vs paper #538 337 places worse
0.7450 ±0.0010
best reported
actual #201 vs paper #538 337 places worse
paper 0.7120 ±0.0050
paper 0.7120 ±0.0050 Δ at pub 0.0330
205
MVGRL+GASSER
0.7448 ±0.0073
This paper
206
GRACE+GASSER
0.7447 ±0.0064
This paper
350
MLP
actual #350 vs paper #867 517 places worse
0.7289 ±0.0010
best reported
actual #350 vs paper #867 517 places worse
paper 0.4931 ±0.0026
paper 0.4931 ±0.0026 Δ at pub 0.2259 Δ today 0.2358
461
AF-GCL
0.7196 ±0.0042
This paper
478
GCL-SPAN
0.7175 ±0.0049
This paper
505
GCA
actual #505 vs paper #528 23 places worse
0.7150 ±0.0030
best reported
actual #505 vs paper #528 23 places worse
paper 0.7133 ±0.0037

Difference within reported uncertainty; not counted as underperformance.

paper 0.7133 ±0.0037 Δ today 0.0017
#ModelAccuracy ↑Paper
1
LGTL
0.9518 ±0.0011
2
MixHop (LO)
0.9513 ±0.0038
3
GraphSAGE (LO)
0.9511 ±0.0036
18
GCN
actual #18 vs paper #571 553 places worse
0.9296 ±0.0015
best reported
actual #18 vs paper #571 553 places worse
paper 0.7916 ±0.0025
116
SAGE
0.8881 ±0.0015
136
CCA-SSG
actual #136 vs paper #340 204 places worse
0.8840 ±0.0060
best reported
actual #136 vs paper #340 204 places worse
paper 0.8160 ±0.0040
paper 0.8160 ±0.0040 Δ at pub 0.0680
144
BGRL
actual #144 vs paper #436 292 places worse
0.8830 ±0.0010
best reported
actual #144 vs paper #436 292 places worse
paper 0.8018 ±0.0063
paper 0.8018 ±0.0063 Δ at pub 0.0812
194
GRACE
actual #194 vs paper #624 430 places worse
0.8730 ±0.0010
best reported
actual #194 vs paper #624 430 places worse
paper 0.7872 ±0.0013
paper 0.7872 ±0.0013 Δ at pub 0.0858
196
MVGRL
actual #196 vs paper #458 262 places worse
0.8725 ±0.0012
best reported
actual #196 vs paper #458 262 places worse
paper 0.7996 ±0.0005
204
DGI
actual #204 vs paper #745 541 places worse
0.8708 ±0.0017
best reported
actual #204 vs paper #745 541 places worse
paper 0.7680 ±0.0060
210
MLP
actual #210 vs paper #844 634 places worse
0.8690 ±0.0074
best reported
actual #210 vs paper #844 634 places worse
paper 0.6914 ±0.0034
paper 0.6914 ±0.0034 Δ at pub 0.1776
243
GCL-SPAN
actual #243 vs paper #552 309 places worse
0.8545 ±0.0016
best reported
actual #243 vs paper #552 309 places worse
paper 0.7927 ±0.0015
paper 0.7927 ±0.0015 Δ today 0.0618
255
GCA
actual #255 vs paper #428 173 places worse
0.8512 ±0.0023
best reported
actual #255 vs paper #428 173 places worse
paper 0.8021 ±0.0039
paper 0.8021 ±0.0039 Δ at pub 0.0107 Δ today 0.0491
281
GRACE+GASSER
0.8397 ±0.0052
This paper
301
GASSER
0.8300 ±0.0061
This paper
302
CCA-SSG+GASSER
0.8300 ±0.0061
This paper
346
AF-GCL
actual #346 vs paper #583 237 places worse
0.8150 ±0.0070
best reported
actual #346 vs paper #583 237 places worse
paper 0.7905 ±0.0075
387
MVGRL+GASSER
0.8080 ±0.0019
This paper
#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
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
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
199
GASSER
0.9317 ±0.0031
This paper
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
275
GCL-SPAN
actual #275 vs paper #392 117 places worse
0.9258 ±0.0017
best reported
actual #275 vs paper #392 117 places worse
paper 0.9124 ±0.0023
paper 0.9124 ±0.0023 Δ today 0.0134
284
AF-GCL
0.9249 ±0.0031
This paper
390
MLP
actual #390 vs paper #535 145 places worse
0.9128 ±0.0063
best reported
actual #390 vs paper #535 145 places worse
paper 0.7853 ±0.0032
paper 0.7853 ±0.0032 Δ at pub 0.1275

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
42
MLP
actual #42 vs paper #179 137 places worse
0.4026 ±0.0108
best reported
actual #42 vs paper #179 137 places worse
paper 0.3617 ±0.0109
paper 0.3617 ±0.0109 Δ at pub 0.0409
68
GraphSAGE
0.3899 ±0.0085
135
GCN
actual #135 vs paper #342 207 places worse
0.3690
best reported
actual #135 vs paper #342 207 places worse
paper 0.3031 ±0.0098
paper 0.3031 ±0.0098 Δ at pub 0.0659
247
MVGRL
actual #247 vs paper #299 52 places worse
0.3464 ±0.0020
best reported
actual #247 vs paper #299 52 places worse
paper 0.3209 ±0.0107
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
paper 0.2827 ±0.0043 Δ at pub 0.0623
282
MVGRL+GASSER
0.3342 ±0.0014
This paper
311
GASSER
0.3147 ±0.0004
This paper
312
CCA-SSG+GASSER
0.3147 ±0.0004
This paper
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
340
GRACE+GASSER
0.3037 ±0.0048
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
357
GCL-SPAN
0.2982 ±0.0010
This paper
361
GCA
actual #361 vs paper #417 56 places worse
0.2965
best reported
actual #361 vs paper #417 56 places worse
paper 0.2635 ±0.0035
375
AF-GCL
0.2894 ±0.0069
This paper
400
CCA-SSG
actual #400 vs paper #417 17 places worse
0.2782 ±0.0060
best reported
actual #400 vs paper #417 17 places worse
paper 0.2635 ±0.0035
paper 0.2635 ±0.0035 Δ today 0.0147
#ModelAccuracy ↑Paper
1
Hetero-S (GAT 8-layer)
0.8693
2
Dir-GNN+CNA
0.8586 ±0.0180
3
GAT
0.8560
27
CCA-SSG
actual #27 vs paper #154 127 places worse
0.7500 ±0.0075
best reported
actual #27 vs paper #154 127 places worse
paper 0.5739 ±0.0138
paper 0.5739 ±0.0138 Δ today 0.1761
34
MVGRL
actual #34 vs paper #172 138 places worse
0.7319 ±0.0042
best reported
actual #34 vs paper #172 138 places worse
paper 0.5381 ±0.0109
52
GCN
actual #52 vs paper #70 18 places worse
0.6796 ±0.0182
actual #52 vs paper #70 18 places worse
paper 0.6796 ±0.0182

Improvement within reported uncertainty; not highlighted.

paper 0.6796 ±0.0182 Δ at pub 0.0036
74
GASSER
0.6723 ±0.0178
This paper
75
CCA-SSG+GASSER
0.6723 ±0.0178
This paper
89
AF-GCL
0.6528 ±0.0053
This paper
95
BGRL
0.6486 ±0.0063
This paper
105
GCA
actual #105 vs paper #154 49 places worse
0.6366 ±0.0032
best reported
actual #105 vs paper #154 49 places worse
paper 0.5739 ±0.0138
paper 0.5739 ±0.0138 Δ at pub 0.0355 Δ today 0.0627
108
SAGE
0.6340 ±0.0300
109
GCL-SPAN
0.6294 ±0.0066
This paper
119
GRACE
actual #119 vs paper #182 63 places worse
0.6124 ±0.0053
best reported
actual #119 vs paper #182 63 places worse
paper 0.5204 ±0.0040
paper 0.5204 ±0.0040 Δ at pub 0.0920
134
DGI
0.6027 ±0.0070
This paper
157
MVGRL+GASSER
0.5658 ±0.0041
This paper
169
MLP
actual #169 vs paper #207 38 places worse
0.5429
best reported
actual #169 vs paper #207 38 places worse
paper 0.4811 ±0.0223
paper 0.4811 ±0.0223 Δ at pub 0.0009 Δ today 0.0618
178
GRACE+GASSER
0.5248 ±0.0013
This paper
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
42
CCA-SSG
actual #42 vs paper #143 101 places worse
0.6158 ±0.0198
best reported
actual #42 vs paper #143 101 places worse
paper 0.4222 ±0.0090
paper 0.4222 ±0.0090 Δ today 0.1936
46
GCN
actual #46 vs paper #75 29 places worse
0.6067
best reported
actual #46 vs paper #75 29 places worse
paper 0.5447 ±0.0117
paper 0.5447 ±0.0117 Δ at pub 0.0123 Δ today 0.0620
50
MVGRL
actual #50 vs paper #177 127 places worse
0.6009 ±0.0044
best reported
actual #50 vs paper #177 127 places worse
paper 0.3875 ±0.0132
83
AF-GCL
0.5210 ±0.0067
This paper
89
GASSER
0.5034 ±0.0056
This paper
90
CCA-SSG+GASSER
0.5034 ±0.0056
This paper
98
GCA
actual #98 vs paper #143 45 places worse
0.4222 ±0.0090
actual #98 vs paper #143 45 places worse
paper 0.4222 ±0.0090

Improvement within reported uncertainty; not highlighted.

paper 0.4222 ±0.0090 Δ at pub 0.0069 Δ today 0.0587
102
GCL-SPAN
0.4723 ±0.0131
This paper
108
BGRL
0.4624 ±0.0070
This paper
120
SAGE
0.4460 ±0.0130
144
DGI
0.4222 ±0.0063
This paper
154
GRACE
actual #154 vs paper #172 18 places worse
0.4109 ±0.0085
best reported
actual #154 vs paper #172 18 places worse
paper 0.3922 ±0.0048
157
MVGRL+GASSER
0.4079 ±0.0029
This paper
172
MLP
actual #172 vs paper #235 63 places worse
0.3930 ±0.0079
best reported
actual #172 vs paper #235 63 places worse
paper 0.3168 ±0.0190
paper 0.3168 ±0.0190 Δ at pub 0.0167 Δ today 0.0762
198
GRACE+GASSER
0.3689 ±0.0082
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