国家自然科学基金(61170112)
北京市自然科学基金(4172016)
北京市教委科技计划一般项目(KM201710011006)
公安部重点实验室开放课题
[1] Tan S L, Guan Z Y, Cai D, et al. Mapping users across networks by manifold alignment on hypergraph. In: Proceedings of the 28th AAAI Conference on Artificial Intelligence, Québec City, 2014. 159--165. Google Scholar
[2] Zhao D, Wang L, Li S. Immunization of Epidemics in Multiplex Networks. PLoS ONE, 2014, 9: e112018 CrossRef PubMed ADS Google Scholar
[3] Wang W, Tang M, Zhang H F. Epidemic spreading on complex networks with general degree and weight distributions. Phys Rev E, 2014, 90: 042803 CrossRef PubMed ADS arXiv Google Scholar
[4] Zhang H F, Shu P P, Tang M, et al. Preferential imitation of vaccinating behavior can invalidate the targeted subsidy on complex network. 2015,. arXiv Google Scholar
[5] Lerman K, Ghosh R. Information contagion: an empirical study of the spread of news on digg and twitter social networks. Comput Sci, 2010, 52: 166--176. Google Scholar
[6] Li R Q, Tang M, Hui P M. Epidemic spreading on multi-relational networks. Journal of Physics, 2013, 62: 504-510 DOI: 10.7498/aps.62.168903. Google Scholar
[7] Cozzo E, Ba?os R A, Meloni S. Contact-based social contagion in multiplex networks. Phys Rev E, 2013, 88: 050801 CrossRef PubMed ADS arXiv Google Scholar
[8] Zhang X. Multilayer networks science: concepts, theories and data. Complex Syst Complex Sci, 2015, 12: 103--107. Google Scholar
[9] Mollgaard A, Zettler I, Dammeyer J, et al. Measure of Node Similarity in Multilayer Networks. 2016,. arXiv Google Scholar
[10] Granell C, Gómez S, Arenas A. Competing spreading processes on multiplex networks: Awareness and epidemics. Phys Rev E, 2014, 90: 012808 CrossRef PubMed ADS arXiv Google Scholar
[11] Zafarani R, Liu H. Connecting users across social media sites: a behavioral-modeling approach. In: Proceedings of the 19th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Chicago, 2013. 41--49. Google Scholar
[12] Zafarani R, Liu H. Connecting corresponding identities across communities. In: Proceedings of the 3rd International AAAI Conference on Weblogs and Social Media, San Jose, 2009. 354--357. Google Scholar
[13] Mikolov T, Sutskever I, Chen K, et al. Distributed representations of words and phrases and their compositionality. In: Proceedings of the 27th Conference on Neural Information Processing Systems, Lake Tahoe, 2013. 3111--3119. Google Scholar
[14] Matsuno R, Murata T. MELL: effective embedding method for multiplex networks. In: Proceedings of the 27th World Wide Web Conference, Lyon, 2018. 1261--1268. Google Scholar
[15] Le Q V, Mikolov T. Distributed representations of sentences and documents. Comput Sci, 2014, 4: 1188--1196. Google Scholar
[16] Perozzi B, Alrfou R, Skiena S. DeepWalk: online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, 2014. 701--710. Google Scholar
[17] Gligorijevic V, Panagakis Y, Zafeiriou S. Non-negative matrix factorizations for multiplex network analysis. IEEE Trans Pattern Anal, 2018, 41: 928--940. Google Scholar
[18] Lee D D, Seung H S. Learning the parts of objects by non-negative matrix factorization. Nature, 1999, 401: 788-791 CrossRef PubMed ADS Google Scholar
[19] Feng T, Li S Z, Shum H Y, et al. Local non-negative matrix factorization as a visual representation. In: Proceedings of the 2nd International Conference on Development and Learning, Cambridge, 2002. 178--183. Google Scholar
[20] Guillamet D, Vitrià J, Schiele B. Introducing a weighted non-negative matrix factorization for image classification. Pattern Recognition Lett, 2003, 24: 2447-2454 CrossRef Google Scholar
[21] Wang Y, Jia Y, Hu C, et al. Fisher non-negative matrix factorization for learning local features. In: Proceedings of the Asian Conference on Computer Vision, Jeju Island, 2004. 27--30. Google Scholar
[22] Gao Y, Church G. Improving molecular cancer class discovery through sparse non-negative matrix factorization.. Bioinformatics, 2005, 21: 3970-3975 CrossRef PubMed Google Scholar
[23] Yi L, Rong J, Liu Y. Semi-supervised multi-label learning by constrained non-negative matrix factorization. In: Proceedings of the 21st National Conference on Artificial Intelligence, Boston, 2006. 421--426. Google Scholar
[24] Carmonasaez P, Pascualmarqui R D, Tirado F, et al. Biclustering of gene expression data by non-smooth non-negativematrix factorization. BMC Bioinform, 2006, 7: 205--208. Google Scholar
[25] Tang J, Qu M, Wang M Z, et al. LINE: large-scale information network embedding. In: Proceedings of the 24th International Conference on World Wide Web, Florence, 2015. 1067--1077. Google Scholar
[26] Grover A, Leskovec J. Node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, 2016. 855--864. Google Scholar
[27] Zhou N, Zhao W X, Zhang X. A General Multi-Context Embedding Model for Mining Human Trajectory Data. IEEE Trans Knowl Data Eng, 2016, 28: 1945-1958 CrossRef Google Scholar
[28] Cui P, Wang X, Pei J. A Survey on Network Embedding. IEEE Trans Knowl Data Eng, 2019, 31: 833-852 CrossRef Google Scholar
[29] Wang D X, Cui P, Zhu W W. Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, 2016. 1225--1234. Google Scholar
[30] Kipf T N, Welling M. Semi-supervised classification with graph convolutional networks. 2016,. arXiv Google Scholar
[31] Hamilton W, Ying Z, Leskovec J. Inductive representation learning on large graphs. In: Proceedings of the 31st Conference on Neural Information Processing Systems, Long Beach, 2017. 1024--1034. Google Scholar
[32] Chen J, Ma T, Xiao C. Fastgcn: fast learning with graph convolutional networks via importance sampling. 2018,. arXiv Google Scholar
[33] Pan S R, Hu R Q, Long G D, et al. Adversarially regularized graph autoencoder for graph embedding. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence, Stockholm, 2018. 2609--2615. Google Scholar
[34] Hinton G E, Salakhutdinov R R. Reducing the Dimensionality of Data with Neural Networks. Science, 2006, 313: 504-507 CrossRef PubMed ADS Google Scholar
[35] Wang H W, Wang J, Wang J L, et al. GraphGAN: graph representation learning with generative adversarial nets. In: Proceedings of the 32nd AAAI Conference on Artificial Intelligence, New Orleans, 2018. 2508--2515. Google Scholar
[36] Goodfellow I, Pouget-Abadie J, Mirza M, et al. Generative adversarial nets. In: Proceedings of the 28th Conference on Neural Information Processing Systems, Montreal, 2014. 2672--2680. Google Scholar
[37] Qu M, Tang J, Shang J B, et al. An attention-based collaboration framework for multi-view network representation learning. In: Proceedings of the 26th ACM International Conference on Information and Knowledge Management, Singapore, 2017. 1767--1776. Google Scholar
[38] Xu L C, Wei X K, Cao J N, et al. Embedding of embedding (eoe): joint embedding for coupled heterogeneous networks. In: Proceedings of the 10th ACM International Conference on Web Search and Data Mining, Cambridge, 2017. 741--749. Google Scholar
[39] Tang J, Cai K K, Su Z, et al. BigNet 2016: first workshop on big network analytics. In: Proceedings of the 25th ACM International on Conference on Information and Knowledge Management, München, 2016. 2505--2506. Google Scholar
[40] Fortunato S. Community detection in graphs. Phys Rep, 2010, 486: 75-174 CrossRef ADS arXiv Google Scholar
[41] Kong X, Zhang J, Yu P S. Inferring anchor links across multiple heterogeneous social networks. In: Proceedings of the 22nd ACM International on Conference on Information and Knowledge Management, New York, 2013. 179--188. Google Scholar
Figure 1
TV drama – film coupling network
Figure 2
Model: CWCNE
Figure 3
Results of community detection in social coupling network. (a) Topology of social coupling network; protectłinebreak (b) visualization of node representation vectors
Figure 4
Modularity contrast of algorithms with different $k$ on film coupling network
Figure 5
The recognition results of the main body of social coupled network
Figure 6
The influence of the known proportion of the coupling nodes on the body recognition
Figure 7
Two label classification P-R curve
Figure 8
The effect of step size on the coupling node vector. (a) Current network step size; (b) coupling network step size
Figure 9
The effect of vector dimension on the coupling node vector
Initialization: Sample $\Phi$ from $\mathbb{R}^{|V_{1}~V_{2}|\times~d}$; |
Build a binary Tree $T$ from $|V_{1}~V_{2}|$; |
$O~=~{\rm~suffle}(|V_{1}~V_{2}|)$; |
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$W_{v_{i}}={\rm RandomWalk}(G,v_{i},t)$; |
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$W_{v_{i}}={\rm concat(RandomWalk}(G,v_{i},t-t'),{\rm RandomWalk}(G,v_{i}',v'))$; |
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${\rm~CouplingSkipGram}(\Phi,W_{v_{i}},\omega,{\rm~CV})$; |
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Dataset | Number of vertexes | Number of edges | Number of vertexes | Number of edges | Number of |
in network 1 | in network 1 | in network 2 | in network 2 | coupling vertexes | |
SCN | 22 | 74 | 25 | 103 | 8 |
ACN | 2985414 | 25965384 | 1053188 | 3916907 | 733592 |
FCN | 9274 | 138065 | 2805 | 293848 | 1947 |
PCN | 3429936 | 27519883 | 92385 | 687327 | 46260 |
WCN | 372971 | 919276 | 17365 | 38247 | 15406 |
MCN | 10000 | 20000 | 10000 | 10000 | 2000 |
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$J(\Phi)=-{\rm~log}{\rm~Pr}(u_{k}|\Phi(v_{j}))$; |
$\Phi~=~\Phi-\alpha~~\frac{\partial~J}{\partial~\Phi}$; |
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$J(\Phi)=-{\rm log}{\rm Pr}(u_{k}|\Phi(v_{j}))$; |
$\Phi~=~\Phi-\alpha~~\frac{\partial~J}{\partial~\Phi}$; |
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Dataset | Deepwalk | Node2vec | LINE | SDNE | CWCNE |
SCN ($k=5$) | 0.334 | 0.345 | 0.274 | 0.312 | 0.381 |
ACN ($k=8$) | 0.396 | 0.431 | 0.337 | 0.423 | 0.426 |
FCN ($k=7$) | 0.383 | 0.408 | 0.372 | 0.392 | 0.490 |
PCN ($k=13$) | 0.435 | 0.443 | 0.391 | 0.413 | 0.391 |
WCN ($k=8$) | 0.351 | 0.385 | 0.349 | 0.391 | 0.373 |
MCN ($k=46$) | 0.524 | 0.507 | 0.493 | 0.537 | 0.598 |
Dataset | Network | Deepwalk | Node2vec | LINE | SDNE | CWCNE |
SCN | SCN1 | 0.349 | 0.355 | 0.294 | 0.337 | 0.358 |
SCN2 | 0.341 | 0.337 | 0.289 | 0.341 | 0.349 | |
ACN | ACN1 | 0.423 | 0.429 | 0.342 | 0.425 | 0.425 |
ACN2 | 0.411 | 0.423 | 0.318 | 0.412 | 0.415 | |
FCN | FCN1 | 0.462 | 0.481 | 0.351 | 0.477 | 0.487 |
FCN2 | 0.468 | 0.479 | 0.357 | 0.472 | 0.479 | |
PCN | PCN1 | 0.440 | 0.460 | 0.403 | 0.429 | 0.463 |
PCN2 | 0.439 | 0.452 | 0.398 | 0.424 | 0.457 | |
WCN | WCN1 | 0.360 | 0.368 | 0.351 | 0.341 | 0.368 |
WCN2 | 0.357 | 0.365 | 0.364 | 0.352 | 0.367 | |
MCN | MCN1 | 0.516 | 0.503 | 0.486 | 0.529 | 0.572 |
MCN2 | 0.504 | 0.491 | 0.481 | 0.523 | 0.548 |
Dataset | Deepwalk | Node2vec | LINE | SDNE | CWCNE |
SCN | 0.187 | 0.187 | 0.174 | 0.192 | 0.250 |
ACN | 0.389 | 0.391 | 0.382 | 0.391 | 0.394 |
FCN | 0.437 | 0.437 | 0.425 | 0.439 | 0.452 |
PCN | 0.692 | 0.687 | 0.673 | 0.698 | 0.735 |
WCN | 0.517 | 0.526 | 0.527 | 0.531 | 0.564 |
MCN | 0.604 | 0.618 | 0.607 | 0.611 | 0.635 |
Dataset (%) | SCN | ACN | FCN | FCN | WCN | MCN |
CWCNE vs. DeepWalk | 6.3** | 0.5 | 1.5** | 4.3** | 4.7** | 3.1** |
CWCNE vs. Node2vec | 6.3** | 0.3 | 1.5** | 4.8** | 3.8** | 1.7** |
CWCNE vs. LINE | 7.6** | 1.2** | 2.7** | 6.2** | 3.7** | 2.8** |
CWCNE vs. SDNE | 5.8** | 0.3** | 1.3** | 3.7** | 3.3 ** | 2.4** |
Dataset | Measure | Deepwalk | Node2vec | LINE | SDNE | CWCNE |
SCN | $P$ | 0.751 | 0.872 | 0.793 | 0.852 | 0.875 |
$R$ | 0.681 | 0.603 | 0.640 | 0.623 | 0.619 | |
$F$1 | 0.714 | 0.712 | 0.708 | 0.720 | 0.725 | |
ACN | $P$ | 0.814 | 0.836 | 0.803 | 0.837 | 0.851 |
$R$ | 0.659 | 0.729 | 0.631 | 0697 | 0.783 | |
$F$1 | 0.728 | 0.778 | 0.707 | 0.761 | 0.815 | |
FCN | $P$ | 0.688 | 0.687 | 0.675 | 0.683 | 0.693 |
$R$ | 0.573 | 0.598 | 0.551 | 0.579 | 0.604 | |
$F$1 | 0.625 | 0.629 | 0.607 | 0.628 | 0.645 | |
PCN | $P$ | 0.937 | 0.922 | 0.908 | 0.925 | 0.950 |
$R$ | 0.892 | 0.872 | 0.883 | 0.868 | 0.895 | |
$F$1 | 0.913 | 0.896 | 0.895 | 0.896 | 0.921 |
Dataset | Measure | Deepwalk | Node2vec | LINE | SDNE | CWCNE |
SCN ($N=9$) | $P$ | 0.276 | 0.301 | 0.283 | 0.298 | 0.307 |
$R$ | 0.201 | 0.248 | 0.237 | 0.246 | 0.246 | |
$F$1 | 0.232 | 0.272 | 0.258 | 0.270 | 0.273 | |
ACN ($N=6$) | $P$ | 0.338 | 0.374 | 0.352 | 0.369 | 0.375 |
$R$ | 0.308 | 0.352 | 0.318 | 0.341 | 0.352 | |
$F$1 | 0.322 | 0.363 | 0.334 | 0.354 | 0.363 | |
PCN ($N=12$) | $P$ | 0.122 | 0.173 | 0.143 | 0.164 | 0.183 |
$R$ | 0.073 | 0.102 | 0.088 | 0.097 | 0.097 | |
$F$1 | 0.091 | 0.128 | 0.109 | 0.122 | 0.128 | |
WCN ($N=8$) | $P$ | 0.325 | 0.321 | 0.315 | 0.322 | 0.336 |
$R$ | 0.179 | 0.183 | 0.168 | 0.173 | 0.185 | |
$F$1 | 0.231 | 0.233 | 0.219 | 0.225 | 0.238 |