ICML 2018

Anonymous Walk Embeddings

Sergey Ivanov, Evgeny Burnaev

Main figure for Anonymous Walk Embeddings

Abstract

The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original problem of network representation in task-agnostic manner. Here, we coherently propose an approach for embedding entire graphs and show that our feature representations with SVM classifier increase classification accuracy of CNN algorithms and traditional graph kernels. For this we describe a recently discovered graph object, anonymous walk, on which we design task-independent algorithms for learning graph representations in explicit and distributed way. Overall, our work represents a new scalable unsupervised learning of state-of-the-art representations of entire graphs.

Proposed method: WL

Benchmark Results

Tested on 3 datasets 1 baseline value reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

TU Dortmund

#ModelAccuracy ↑Paper
1
MSH-GNN
0.9910 ±0.0030
2
ID-GNN+BEC
0.9830 ±0.0360
3
SupCosine
0.9830 ±0.0250
39
GIN
0.9330 ±0.0290
51
PSCN
0.9263 ±0.0421
This paper
159
WL
actual #159 vs paper #596 437 places worse
0.9040 ±0.0570
best reported
actual #159 vs paper #596 437 places worse
paper 0.8072 ±0.0300
paper 0.8072 ±0.0300 Δ at pub 0.0528 Δ today 0.0968
341
AWE
0.8787 ±0.0976
This paper
365
DGK
actual #365 vs paper #539 174 places worse
0.8744 ±0.0272
best reported
actual #365 vs paper #539 174 places worse
paper 0.8266 ±0.0145
paper 0.8266 ±0.0145 Δ today 0.0478
403
MLP
0.8660 ±0.0495
506
GK
actual #506 vs paper #580 74 places worse
0.8350 ±0.0060
best reported
actual #506 vs paper #580 74 places worse
paper 0.8158 ±0.0211

Difference within reported uncertainty; not counted as underperformance.

paper 0.8158 ±0.0211 Δ today 0.0192
614
KR
0.8005 ±0.0164
This paper
752
ER
0.7189 ±0.0066
This paper
#ModelAccuracy ↑Paper
1
WL-MLP
0.9792
2
MSH-GNN
0.9640 ±0.0070
3
CoCN
0.8722 ±0.0013
23
GCN
0.8260 ±0.0220
151
MLP
0.7920 ±0.0240
153
WL
actual #153 vs paper #155 2 places worse
0.7910 ±0.0010
best reported
actual #153 vs paper #155 2 places worse
paper 0.7902 ±0.0177

Difference within reported uncertainty; not counted as underperformance.

paper 0.7902 ±0.0177 Δ at pub 0.0008
266
AWE (DD)
0.7393 ±0.0194
This paper
267
AWE (DD) RBF
0.7393
This paper
269
AWE (DD) Inner
0.7377
This paper
274
DGK
actual #274 vs paper #275 1 place worse
0.7310 ±0.0030
best reported
actual #274 vs paper #275 1 place worse
paper 0.7309 ±0.0025

Difference within reported uncertainty; not counted as underperformance.

paper 0.7309 ±0.0025 Δ today 0.0001
277
GK
0.7284 ±0.0028
This paper
293
AWE (FB) RBF
0.7099
This paper
298
AWE (DD) Poly
0.7045
This paper
304
AWE (FB) Inner
0.6960
This paper
323
AWE (FB) Poly
0.6430
This paper
#ModelAccuracy ↑Paper
1
GMN
0.7866
2
MemGNN
0.7550
3
TFGW SP
0.7510 ±0.0500
17
GatedGCN
0.7000 ±0.0494
18
WL
actual #18 vs paper #145 127 places worse
0.6950 ±0.0320
best reported
actual #18 vs paper #145 127 places worse
paper 0.5315 ±0.0114
paper 0.5315 ±0.0114 Δ at pub 0.0590 Δ today 0.1635
26
GraphSAGE
0.6817 ±0.0545
124
MLP
0.5583 ±0.0352
145
DGK
actual #145 vs paper #246 101 places worse
0.5343 ±0.0091
best reported
actual #145 vs paper #246 101 places worse
paper 0.2708 ±0.0079
paper 0.2708 ±0.0079 Δ at pub 0.2635
169
AWE
actual #169 vs paper #205 36 places worse
0.4558 ±0.0211
best reported
actual #169 vs paper #205 36 places worse
paper 0.3577 ±0.0593
paper 0.3577 ±0.0593 Δ today 0.0981
218
GK
actual #218 vs paper #218
0.3270 ±0.0120
actual #218 vs paper #218
paper 0.3270 ±0.0120
paper 0.3270 ±0.0120 Δ at pub 0.0609
232
KR
0.3001 ±0.0101
This paper
303
ER
0.1497 ±0.0028
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 Best today — OK at publication; today's leaderboard best is elsewhere