Localized Graph Contrastive Learning

Hengrui Zhang, Qitian Wu, Yu Wang, Shaofeng Zhang, Junchi Yan, Philip S. Yu

Main figure for Localized Graph Contrastive Learning

Abstract

Contrastive learning methods based on InfoNCE loss are popular in node representation learning tasks on graph-structured data. However, its reliance on data augmentation and its quadratic computational complexity might lead to inconsistency and inefficiency problems. To mitigate these limitations, in this paper, we introduce a simple yet effective contrastive model named Localized Graph Contrastive Learning (in short). consists of two key designs: 1) We fabricate the positive examples for each node directly using its first-order neighbors, which frees our method from the reliance on carefully-designed graph augmentations; 2) To improve the efficiency of contrastive learning on graphs, we devise a kernelized contrastive loss, which could be approximately computed in linear time and space complexity with respect to the graph size. We provide theoretical analysis to justify the effectiveness and rationality of the proposed methods. Experiments on various datasets with different scales and properties demonstrate that in spite of its simplicity, achieves quite competitive performance in self-supervised node representation learning tasks on graphs with various scales and properties.

Proposed method: kernelized contrastive loss computation

Benchmark Results

Tested on 4 datasets 9 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
0.9669 ±0.0014
3
GAT+T
0.9660 ±0.0007
7
SAGE
0.9643 ±0.0027
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
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 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.9307 ±0.0028 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
188
Local-GCL
0.9325 ±0.0040
This paper
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
194
SUGRL
actual #194 vs paper #214 20 places worse
0.9307 ±0.0015
actual #194 vs paper #214 20 places worse
paper 0.9307 ±0.0015

Improvement within reported uncertainty; not highlighted.

paper 0.9307 ±0.0015 Δ at pub 0.0022
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
284
AF-GCL
0.9249 ±0.0031
This paper
390
MLP
0.9128 ±0.0063
408
GMI
actual #408 vs paper #413 5 places worse
0.9073 ±0.0024
actual #408 vs paper #413 5 places worse
paper 0.9073 ±0.0024

Improvement within reported uncertainty; not highlighted.

paper 0.9073 ±0.0024 Δ at pub 0.0001
#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
79
BGRL
actual #79 vs paper #125 46 places worse
0.9034 ±0.0019
best reported
actual #79 vs paper #125 46 places worse
paper 0.8969 ±0.0037
paper 0.8969 ±0.0037 Δ at pub 0.0065 Δ today 0.0065
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 0.0328 Δ today 0.0328
159
CCA-SSG
actual #159 vs paper #171 12 places worse
0.8896 ±0.0013
best reported
actual #159 vs paper #171 12 places worse
paper 0.8874 ±0.0028

Difference within reported uncertainty; not counted as underperformance.

paper 0.8874 ±0.0028 Δ today 0.0022
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
actual #162 vs paper #162
paper 0.8893 ±0.0021

Improvement within reported uncertainty; not highlighted.

paper 0.8893 ±0.0021 Δ at pub 0.0002
169
kernelized contrastive loss computation
0.8881 ±0.0037
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
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
320
MLP
0.8463
342
GMI
actual #342 vs paper #342
0.8422 ±0.0052
actual #342 vs paper #342
paper 0.8422 ±0.0052

Improvement within reported uncertainty; not highlighted.

paper 0.8422 ±0.0052 Δ at pub 0.0201
#ModelAccuracy ↑Paper
1
GrokFormer
0.9831 ±0.0018
2
PolyFormer
0.9808 ±0.0027
3
SGFormer
0.9796 ±0.0081
9
GCN
0.9774 ±0.0035
47
Local-GCL
0.9633 ±0.0013
This paper
58
MLP
0.9597 ±0.0007
69
BGRL
actual #69 vs paper #122 53 places worse
0.9580 ±0.0040
best reported
actual #69 vs paper #122 53 places worse
paper 0.9548 ±0.0008

Difference within reported uncertainty; not counted as underperformance.

paper 0.9548 ±0.0008 Δ at pub 0.0032
106
CCA-SSG
actual #106 vs paper #133 27 places worse
0.9559 ±0.0007
best reported
actual #106 vs paper #133 27 places worse
paper 0.9538 ±0.0006
paper 0.9538 ±0.0006 Δ at pub 0.0021
125
MVGRL
actual #125 vs paper #134 9 places worse
0.9544 ±0.0027
best reported
actual #125 vs paper #134 9 places worse
paper 0.9533 ±0.0003

Difference within reported uncertainty; not counted as underperformance.

paper 0.9533 ±0.0003 Δ today 0.0011
134
SUGRL
0.9538 ±0.0011
This paper
154
AF-GCL
0.9512 ±0.0015
This paper
167
DGI
actual #167 vs paper #174 7 places worse
0.9489 ±0.0009
best reported
actual #167 vs paper #174 7 places worse
paper 0.9451 ±0.0052

Difference within reported uncertainty; not counted as underperformance.

paper 0.9451 ±0.0052 Δ at pub 0.0006 Δ today 0.0038

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
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
271
Local-GCL
0.3391 ±0.0057
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
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 at pub 0.0076
375
AF-GCL
0.2894 ±0.0069
This paper
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 at pub 0.0054
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