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Table 2 Results of influence attacks against each classifier with the Cora dataset, with attacker budgets of 10, 30, and 50 edge perturbations

From: Complex network effects on the robustness of graph convolutional networks

  

Budget 10

Budget 30

Budget 50

Defense

Training

Net

FGA

IG

Net

FGA

IG

Net

FGA

IG

Jaccard

Rand.

0.296

0.24

N/A

0.472

0.432

N/A

0.592

0.504

N/A

Jaccard

SD

0.264

0.192

N/A

0.352

0.312

N/A

0.4

0.424

N/A

Jaccard

GC

0.224

0.256

N/A

0.36

0.392

N/A

0.448

0.456

N/A

RGCN

Rand.

0.68

0.6

N/A

0.912

0.944

N/A

0.952

0.976

N/A

RGCN

SD

0.448

0.408

N/A

0.848

0.784

N/A

0.904

0.888

N/A

RGCN

GC

0.44

0.296

N/A

0.832

0.808

N/A

0.92

0.888

N/A

Cheb

Rand.

0.448

0.448

N/A

0.784

0.808

N/A

0.872

0.896

N/A

Cheb

SD

0.656

0.48

N/A

0.976

0.816

N/A

0.976

0.912

N/A

Cheb

GC

0.488

0.448

N/A

0.864

0.88

N/A

0.928

0.912

N/A

SVD

Rand.

0.224

0.32

N/A

0.536

0.72

N/A

0.76

0.872

N/A

SVD

SD

0.296

0.216

N/A

0.568

0.536

N/A

0.76

0.728

N/A

SVD

GC

0.264

0.264

N/A

0.584

0.528

N/A

0.84

0.768

N/A

median

Rand.

0.544

0.424

N/A

0.872

0.808

N/A

0.944

0.912

N/A

median

SD

0.4

0.424

N/A

0.8

0.784

N/A

0.912

0.888

N/A

median

GC

0.24

0.312

N/A

0.784

0.84

N/A

0.896

0.912

N/A

GAT

Rand.

0.544

0.552

N/A

0.904

0.88

N/A

0.96

0.952

N/A

GAT

SD

0.608

0.48

N/A

0.88

0.816

N/A

0.968

0.872

N/A

GAT

GC

0.48

0.352

N/A

0.872

0.768

N/A

0.952

0.952

N/A

GCN

Rand.

0.568

0.448

N/A

0.896

0.896

N/A

0.936

0.952

N/A

GCN

SD

0.456

0.32

N/A

0.752

0.696

N/A

0.856

0.872

N/A

GCN

GC

0.384

0.32

N/A

0.816

0.776

N/A

0.896

0.896

N/A

SGC

Rand.

0.568

N/A

N/A

0.824

N/A

N/A

0.888

N/A

N/A

SGC

SD

0.632

N/A

N/A

0.84

N/A

N/A

0.856

N/A

N/A

SGC

GC

0.584

N/A

N/A

0.824

N/A

N/A

0.88

N/A

N/A

  1. Results are included for Nettack (Net), FGA, and IG-FGSM (IG). For each classifier, we train with random (Rand.), StratDegree (SD), and GreedyCover (GC). Each entry is a probability of attack success, thus higher is better for the attacker and lower is better for the defender. To yield the most robust classifier, the defender picks the classifier/training method combination that minimizes the worst-case attack probability. These entries are listed in bold. Entries representing the most robust case for random training are in italic. Entries listed as N/A did not finish in the allotted time (24 h per trial). The Jaccard-based classifier performs best, both overall and using random training. If we focus on classifiers that achieve the best performance in Fig. 8, (i.e., omitting Jaccard and SVD), the best performance is achieved by GCNs with the alternative training methods