IEEE Computational Intelligence Magazine - May 2023 - 55

TABLE II The experimental results obtained on various datasets. The " - " symbol indicates that the corresponding algorithm
is unable to execute on this network.
SND
NMI
ARI
ACC
WTN
NMI
ARI
ACC
CoRA
NMI
ARI
ACC
CiteSeer
NMI
ARI
ACC
Syn1
NMI
ARI
ACC
Syn2
Syn3
NMI
ARI
ACC
NMI
ARI
ACC
MOEA-CPI
0.808
0.773
0.944
0.341
0.201
0.352
0.824
0.856
0.924
0.349
0.339
0.545
1
1
1
1
1
1
0.983
0.926
0.973
MOEA-MultiNet SS-MOML COMCLUS S2-jNMF CSNMF SCML MIMOSA GMC
0.721
0.747
0.732
0.437
0.201
0.465
0.140
0.052
0.389
0.263
0.178
-
-
-
0.461
0.287
0.46
-
-
-
-
-
-
0.316
0.197
0.306
0.886
0.924
0.932
0.345
0.337
0.532
0.930
0.915
0.96
0.965
0.972
0.936
0.953
0.895
0.931
0.555
0.480
0.944
0.183
0.105
0.478
0.471
0.447
0.719
0.182
0.119
0.385
1
1
1
0.950
0.902
0.98
0.894
0.814
0.892
0.582
0.452
0.928
0.157
0.069
0.437
0.769
0.813
0.569
0.149
0.147
0.188
0.507
0.404
0.67
0.681
0.493
0.928
0.284
0.197
0.568
0.514
0.491
0.916
0.237
0.207
0.178
0.406
0.325
0.44
0.681
0.493
0.718
0.231
0.129
0.415
0.480
0.485
0.704
0.191
0.169
0.411
0.688
0.592
0.81
0.132
0.088
0.704
-
-
-
0.011
0.001
0.343
-
-
-
0.690
0.573
0.75
0.772 11 0.855
0.602 11 0.896
0.76 11 0.912
0.975
0.879
0.911
0.946
0.874
0.837
1
1
1
0.098
0.01
0.102
0.597
0.428
0.704
0.203
0.015
0.389
0.519
0.426
0.883
0.042
0.012
0.216
0.754
0.691
0.87
1
1
1
0.963
0.954
0.98
B. Baselines and Parameter Settings
To evaluate the performance of the proposed MOEA-CPI
approach,thispaper selectsdifferent kindsofstate-of-the-art
methodsascomparisonalgorithms. More specifically, optimization-based
methods (i.e., MOEA-MultiNet [6] and SSMOML
[28]), NMF-based methods (i.e., COMCLUS [5], S2jNMF
[1] and CSNMF [4]), spectral clustering methods (i.e., SCML
[17] and MIMOSA [47]) and multiview clustering methods
(i.e., GMC [48]) are tested. To ensure the fairness of the experiment,
the parameter settings ofthe comparison algorithms remain
consistent with those oftheir source papers. All EA results are averaged
over 100 times to eliminate fluctuations.
Two main parameters of the MOEA-CPI algorithm control
the importance of the prior information, where Cos and
Jac determine the reservation proportion of the graph-level
and node-level information. In the experiment, the parameters
are set as Cos ¼f0:2; 0:3g andJac ¼f0:1; 0:2g, and the analysis
ofthese two parameters is shown in Section IV-D.
C. Experimental Results
1) Overall Experiment Results
Table II shows the results ofan accuracy comparison between the
proposed MOEA-CPI approach and eight other state-of-the-art
comparison algorithms running on different multilayer networks
as measured by three widely used metrics, i.e., the NMI, ARI,
and accuracy (ACC) [5].Asshown in Table II, the clustering performance
of the MOEA-CPI approach proposed in this paper is
significantly better than that ofthe other methods. Quantitatively,
taking the NMI metric as an example, the NMI values of
MOEA-CPI are improved by 43.7%, 36.1%, 66.3%, and 15.1%
over those of the optimization-based algorithms (MOEA-MultiNet
and SS-MOML), NMF-based algorithms (COMCLUS, S2jNMF,
and CSNMF), spectral-based algorithms (SC-ML and
MIMOSA), and multiview-based algorithm (GMC), respectively.
In terms of specific algorithms, although CSNMF can fuse the
information of each layer into a consensus representation to best
utilize the network information, our proposed MOEA-CPI
method still achieves a significant improvement over CSNMF,
especially on the SND, Cora, and Citeseer. MOEA-MultiNet
and SS-MOML apply different objective functions, which adapt
better to different network structures. As described in the experimental
results, MOEA-CPI produces comparatively obvious
improvements on most datasets except CoRA. In addition,
MIMOSA cannot address Citeseer since the network is not fully
connected. Similarly,MOEA-MultiNet cannot address large-scale
networks effectively due to its high time consumption level.
Despite the sparse structure of Citeseer, through the combined
effects of the weighting strategy, MOEA and consensus prior
information, MOEA-CPI still achieves outstanding accuracy in
MAY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 55
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