Barlow Graph Auto-Encoder for Unsupervised Network Embedding

R. A. Khan, M. Kleinsteuber

Main figure for Barlow Graph Auto-Encoder for Unsupervised Network Embedding

Abstract

Network embedding has emerged as a promising research field for network analysis. Recently, an approach, named Barlow Twins, has been proposed for self-supervised learning in computer vision by applying the redundancy-reduction principle to the embedding vectors corresponding to two distorted versions of the image samples. Motivated by this, we propose Barlow Graph Auto-Encoder, a simple yet effective architecture for learning network embedding. It aims to maximize the similarity between the embedding vectors of immediate and larger neighborhoods of a node, while minimizing the redundancy between the components of these projections. In addition, we also present the variation counterpart named as Barlow Variational Graph Auto-Encoder. Our approach yields promising results for inductive link prediction and is also on par with state of the art for clustering and downstream node classification, as demonstrated by extensive comparisons with several well-known techniques on three benchmark citation datasets.

Benchmark Results

Tested on 4 datasets 2 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
172
BGRL
actual #172 vs paper #231 59 places worse
0.9337 ±0.0021
best reported
actual #172 vs paper #231 59 places worse
paper 0.9287
paper 0.9287 Δ today 0.0050
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
paper 0.9253 Δ at pub 0.0060 Δ today 0.0067
203
GRACE
actual #203 vs paper #324 121 places worse
0.9215
actual #203 vs paper #324 121 places worse
paper 0.9215
paper 0.9215 Δ at pub 0.1035 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
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
262
ARGA
0.9268
This paper
267
G-BT
0.9263
This paper
285
ARVGA
0.9249
This paper
317
VGAE
actual #317 vs paper #317
0.9224
actual #317 vs paper #317
paper 0.9224

Improvement within reported uncertainty; not highlighted.

paper 0.9224 Δ at pub 0.0004
329
GIC
0.9211
This paper
351
BGAE + Att
0.9189
This paper
352
GAE
actual #352 vs paper #364 12 places worse
0.9168
actual #352 vs paper #364 12 places worse
paper 0.9168

Improvement within reported uncertainty; not highlighted.

paper 0.9168 Δ at pub 0.0006 Δ today 0.0017
390
MLP
0.9128 ±0.0063
401
BGAE
0.9110
This paper
408
GMI
actual #408 vs paper #417 9 places worse
0.9081 ±0.0015
best reported
actual #408 vs paper #417 9 places worse
paper 0.9068

Difference within reported uncertainty; not counted as underperformance.

paper 0.9068 Δ today 0.0013
444
DeepWalk
actual #444 vs paper #444
0.9005
actual #444 vs paper #444
paper 0.9005
paper 0.9005 Δ at pub 0.0061
451
BVGAE + Att
0.8998
This paper
467
BVGAE
0.8938
This paper
537
Raw
0.7853
This paper
#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
17
BGAE + Att
0.9244
This paper
23
BGAE
0.9224
This paper
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 0.8968
paper 0.8968 Δ today 0.0066
110
BVGAE + Att
0.8991
This paper
139
GRACE
actual #139 vs paper #237 98 places worse
0.8953 ±0.0035
best reported
actual #139 vs paper #237 98 places worse
paper 0.8746
paper 0.8746 Δ today 0.0207
150
BVGAE
0.8919
This paper
160
GCA
actual #160 vs paper #160
0.8894
actual #160 vs paper #160
paper 0.8894
paper 0.8894 Δ at pub 0.0073
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
202
G-BT
0.8814
This paper
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
246
VGAE
actual #246 vs paper #272 26 places worse
0.8644
actual #246 vs paper #272 26 places worse
paper 0.8644

Improvement within reported uncertainty; not highlighted.

paper 0.8644 Δ at pub 0.0007 Δ today 0.0077
264
GAE
actual #264 vs paper #307 43 places worse
0.8666 ±0.0007
best reported
actual #264 vs paper #307 43 places worse
paper 0.8518
paper 0.8518 Δ at pub 0.0009 Δ today 0.0148
278
DeepWalk
actual #278 vs paper #278
0.8628
actual #278 vs paper #278
paper 0.8628

Improvement within reported uncertainty; not highlighted.

paper 0.8628 Δ at pub 0.0060
288
ARVGA
actual #288 vs paper #319 31 places worse
0.8602 ±0.0011
best reported
actual #288 vs paper #319 31 places worse
paper 0.8466
293
ARGA
actual #293 vs paper #334 41 places worse
0.8586 ±0.0011
best reported
actual #293 vs paper #334 41 places worse
paper 0.8439
315
GIC
0.8489
This paper
320
MLP
0.8463
342
GMI
actual #342 vs paper #398 56 places worse
0.8422 ±0.0052
best reported
actual #342 vs paper #398 56 places worse
paper 0.8221
paper 0.8221 Δ today 0.0201
457
Raw
0.7381
This paper
#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
58
MLP
0.9597 ±0.0007
63
GCA
actual #63 vs paper #80 17 places worse
0.9590 ±0.0020
best reported
actual #63 vs paper #80 17 places worse
paper 0.9573

Difference within reported uncertainty; not counted as underperformance.

paper 0.9573 Δ today 0.0017
69
BGRL
actual #69 vs paper #109 40 places worse
0.9580 ±0.0040
best reported
actual #69 vs paper #109 40 places worse
paper 0.9556

Difference within reported uncertainty; not counted as underperformance.

paper 0.9556 Δ today 0.0024
77
GRACE
actual #77 vs paper #169 92 places worse
0.9574 ±0.0006
best reported
actual #77 vs paper #169 92 places worse
paper 0.9470
paper 0.9470 Δ today 0.0104
95
BGAE + Att
0.9564
This paper
103
BVGAE + Att
0.9560
This paper
125
MVGRL
actual #125 vs paper #260 135 places worse
0.9544 ±0.0027
best reported
actual #125 vs paper #260 135 places worse
paper 0.9211
141
G-BT
actual #141 vs paper #157 16 places worse
0.9525 ±0.0013
best reported
actual #141 vs paper #157 16 places worse
paper 0.9507

Difference within reported uncertainty; not counted as underperformance.

paper 0.9507 Δ today 0.0018
146
GAE
actual #146 vs paper #161 15 places worse
0.9520 ±0.0010
best reported
actual #146 vs paper #161 15 places worse
paper 0.9492
153
BVGAE
0.9513
This paper
158
BGAE
0.9501
This paper
163
DeepWalk
actual #163 vs paper #163
0.9490
actual #163 vs paper #163
paper 0.9490
paper 0.9490 Δ at pub 0.0313
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
174
VGAE
0.9452
This paper
181
ARGA
actual #181 vs paper #232 51 places worse
0.9432 ±0.0004
best reported
actual #181 vs paper #232 51 places worse
paper 0.9310
183
ARVGA
0.9430
This paper
212
Raw
0.9358
This paper
235
GIC
0.9310
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
94
GRACE
0.8014
This paper
100
BGRL
actual #100 vs paper #100
0.8000 ±0.0010
best reported
actual #100 vs paper #100
paper 0.7998

Difference within reported uncertainty; not counted as underperformance.

paper 0.7998 Δ today 0.0002
112
BGAE + Att
0.7953
This paper
140
BGAE
0.7893
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

Difference within reported uncertainty; not counted as underperformance.

paper 0.7535 Δ today 0.0330
162
GCA
actual #162 vs paper #168 6 places worse
0.7840 ±0.0013
best reported
actual #162 vs paper #168 6 places worse
paper 0.7823

Difference within reported uncertainty; not counted as underperformance.

paper 0.7823 Δ at pub 0.0012 Δ today 0.0017
181
GAE
actual #181 vs paper #265 84 places worse
0.7787 ±0.0053
best reported
actual #181 vs paper #265 84 places worse
paper 0.7015
paper 0.7015 Δ today 0.0772
180
VGAE
actual #180 vs paper #222 42 places worse
0.7787 ±0.0053
best reported
actual #180 vs paper #222 42 places worse
paper 0.7563
paper 0.7563 Δ today 0.0224
183
BVGAE + Att
0.7782
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

Difference within reported uncertainty; not counted as underperformance.

paper 0.7752 Δ today 0.0005
192
BVGAE
0.7752
This paper
197
GIC
0.7728
This paper
198
DeepWalk
actual #198 vs paper #198
0.7721
actual #198 vs paper #198
paper 0.7721

Improvement within reported uncertainty; not highlighted.

paper 0.7721 Δ at pub 0.0286
211
G-BT
actual #211 vs paper #212 1 place worse
0.7683 ±0.0073
best reported
actual #211 vs paper #212 1 place worse
paper 0.7665

Difference within reported uncertainty; not counted as underperformance.

paper 0.7665 Δ today 0.0018
234
GMI
actual #234 vs paper #234
0.7490 ±0.0010
best reported
actual #234 vs paper #234
paper 0.7485

Difference within reported uncertainty; not counted as underperformance.

paper 0.7485 Δ today 0.0005
237
MLP
0.7469 ±0.0085
253
Raw
0.7198
This paper
278
ARVGA
0.6737
This paper
287
ARGA
0.6688
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