From Overfitting to Robustness: Quantity, Quality, and Variety Oriented Negative Sample Selection in Graph Contrastive Learning

Adnan Ali, Jinlong Li, Huanhuan Chen, Ali Kashif Bashir

Main figure for From Overfitting to Robustness: Quantity, Quality, and Variety Oriented Negative Sample Selection in Graph Contrastive Learning

Abstract

Graph contrastive learning (GCL) aims to contrast positive-negative counterparts to learn the node embeddings, whereas graph data augmentation methods are employed to generate these positive-negative samples. The variation, quantity, and quality of negative samples compared to positive samples play crucial roles in learning meaningful embeddings for node classification downstream tasks. Less variation, excessive quantity, and low-quality negative samples cause the model to be overfitted for particular nodes, resulting in less robust models. To solve the overfitting problem in the GCL paradigm, this study proposes a novel Cumulative Sample Selection (CSS) algorithm by comprehensively considering the quality, variations, and quantity of negative samples. Initially, three negative sample pools are constructed: easy, medium, and hard negative samples, which contain 25\ Then, 10\ After that, a decision agent module evaluates model training results and decides whether to explore more negative samples from three negative sample pools by increasing the ratio or keep exploiting the current sampling ratio. The proposed algorithm is integrated into a proposed graph contrastive learning framework named NegAmplify. NegAmplify is compared with the SOTA methods on nine graph node classification datasets, with seven achieving better node classification accuracy with up to 2.86\ NegAmplify is available at:.

Benchmark Results

Tested on 4 datasets 5 baseline values reported too low Non-standard metric on 1 dataset

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
92
LG2AR
0.9410 ±0.0040
This paper
97
NegAmplify_r
0.9409 ±0.0039
This paper
113
ProGCL
actual #113 vs paper #128 15 places worse
0.9381 ±0.0048
best reported
actual #113 vs paper #128 15 places worse
paper 0.9364 ±0.0013

Difference within reported uncertainty; not counted as underperformance.

paper 0.9364 ±0.0013 Δ at pub 0.0017
121
NegAmplify_c
0.9373 ±0.0021
This paper
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
149
ABGML
actual #149 vs paper #156 7 places worse
0.9350 ±0.0040
best reported
actual #149 vs paper #156 7 places worse
paper 0.9346 ±0.0036

Difference within reported uncertainty; not counted as underperformance.

paper 0.9346 ±0.0036 Δ today 0.0004
172
BGRL
actual #172 vs paper #198 26 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #198 26 places worse
paper 0.9317 ±0.0030

Difference within reported uncertainty; not counted as underperformance.

paper 0.9317 ±0.0030 Δ at pub 0.0020
191
GCA
actual #191 vs paper #277 86 places worse
0.9320 ±0.0060
best reported
actual #191 vs paper #277 86 places worse
paper 0.9253 ±0.0016
203
GRACE
actual #203 vs paper #244 41 places worse
0.9313 ±0.0017
best reported
actual #203 vs paper #244 41 places worse
paper 0.9278 ±0.0045

Difference within reported uncertainty; not counted as underperformance.

paper 0.9278 ±0.0045 Δ at pub 0.0002 Δ today 0.0035
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
paper 0.9174 ±0.0007 Δ at pub 0.0136
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
284
AF-GCL
0.9249 ±0.0031
This paper
390
MLP
0.9128 ±0.0063
420
AdaS
0.9063 ±0.0113
This paper
447
DW+F
0.9005 ±0.0008
This paper
465
DW
0.8944 ±0.0011
This paper
540
rf
0.7853
This paper
#ModelAccuracy ↑Paper
1
GCN
0.9302 ±0.0011
2
RSE + RGCN (70b)
0.8852 ±0.0019
3
LEMP+T
0.8825
9
SAGE
0.8771
63
NegAmplify_r
0.8204 ±0.1000
This paper
67
NegAmplify_c
0.8169 ±0.1000
This paper
94
GRACE
0.8014 ±0.4800
This paper
100
BGRL
actual #100 vs paper #100
0.8000 ±0.0010
best reported
actual #100 vs paper #100
paper 0.7998 ±0.1000

Difference within reported uncertainty; not counted as underperformance.

paper 0.7998 ±0.1000 Δ at pub 0.0002 Δ today 0.0002
129
COSTA
0.7912 ±0.0200
This paper
133
AF-GCL
0.7901 ±0.5100
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 ±0.4900

Difference within reported uncertainty; not counted as underperformance.

paper 0.7762 ±0.4900 Δ today 0.0128
149
ABGML
0.7870 ±0.5600
This paper
150
ProGCL
0.7868 ±0.1200
This paper
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 ±0.1400

Difference within reported uncertainty; not counted as underperformance.

paper 0.7535 ±0.1400 Δ at pub 0.0005 Δ today 0.0330
162
GCA
actual #162 vs paper #163 1 place worse
0.7840 ±0.0013
best reported
actual #162 vs paper #163 1 place worse
paper 0.7835 ±0.0500

Difference within reported uncertainty; not counted as underperformance.

paper 0.7835 ±0.0500 Δ at pub 0.0005 Δ today 0.0005
184
LG2AR
0.7780 ±0.5000
This paper
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 ±0.0800

Difference within reported uncertainty; not counted as underperformance.

paper 0.7752 ±0.0800 Δ today 0.0005
201
DW+F
0.7721 ±0.0300
This paper
237
MLP
0.7469 ±0.0085
241
DW
0.7435 ±0.0600
This paper
257
rf
0.7198
This paper

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 #340 89 places worse
0.3450 ±0.0110
best reported
actual #251 vs paper #340 89 places worse
paper 0.3033 ±0.0077
paper 0.3033 ±0.0077 Δ at pub 0.0417
323
NegAmplify_c
0.3114 ±0.0066
This paper
338
NegAmplify_r
0.3047 ±0.0009
This paper
356
BGRL
actual #356 vs paper #404 48 places worse
0.2986
best reported
actual #356 vs paper #404 48 places worse
paper 0.2764 ±0.0003

Heterogeneous Graph Benchmarks

DBLP

Global leaderboard →
Non-default metric. This paper reports Accuracy; the dataset default is Micro-F1. Values below use Accuracy only.

Sorted by Accuracy. Highlighted rows are from other papers.

#ModelAccuracy ↑Paper
1
HG-SCM
0.9490 ±0.0015
2
SeHGNN
0.9489 ±0.0018
3
AdvSynGNN
0.9486 ±0.0012
34
DGI
actual #34 vs paper #55 21 places worse
0.8800 ±0.0020
best reported
actual #34 vs paper #55 21 places worse
paper 0.8320 ±0.0010
paper 0.8320 ±0.0010 Δ at pub 0.0480
36
GCN
0.8758 ±0.0020
43
NegAmplify_r
0.8587 ±0.0005
This paper
45
NegAmplify_c
0.8540 ±0.0004
This paper
50
GRAM
0.8470 ±0.0010
This paper
51
COSTA
0.8450 ±0.0010
This paper
54
GRACE
0.8420 ±0.0010
This paper
55
BGRL
0.8407 ±0.0023
This paper
65
MLP
0.8118 ±0.0020
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