{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T21:43:31Z","timestamp":1780955011184,"version":"3.54.1"},"reference-count":137,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:00:00Z","timestamp":1740182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62202200, U22A2098, 62172185, 62307006, 62206105, 62402197"],"award-info":[{"award-number":["62202200, U22A2098, 62172185, 62307006, 62206105, 62402197"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2021ZD0112500"],"award-info":[{"award-number":["2021ZD0112500"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Key Science and Technology Development Plan of Jilin Province","award":["20240302078GX"],"award-info":[{"award-number":["20240302078GX"]}]},{"name":"Innovation Team Project of Colleges in Guangdong Province","award":["2022KCXTD057"],"award-info":[{"award-number":["2022KCXTD057"]}]},{"name":"Ministry of Education Humanities and Social Sciences Research Planning Fund Project","award":["23YJAZH212"],"award-info":[{"award-number":["23YJAZH212"]}]},{"name":"Foundation of State Key Laboratory of Public Big Data","award":["PBD2022-07"],"award-info":[{"award-number":["PBD2022-07"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Knowl. Discov. Data"],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>Complex networks enable to represent and characterize the interactions between entities in various complex systems which widely exist in the real world and usually generate vast amounts of data about all the elements, their behaviors and interactions over time. The studies concentrating on new network analysis approaches and methodologies are vital because of the diversity and ubiquity of complex networks. The stochastic block model (SBM), based on Bayesian theory, is a statistical network model. SBMs are essential tools for analyzing complex networks since SBMs have the advantages of interpretability, expressiveness, flexibility and generalization. Thus, designing diverse SBMs and their learning algorithms for various networks has become an intensively researched topic in network analysis and data mining. In this article, we review, in a comprehensive and in-depth manner, SBMs for different types of networks (i.e., model extensions), existing methods (including parameter estimation and model selection) for learning optimal SBMs for given networks and SBMs combined with deep learning. Finally, we provide an outlook on the future research directions of SBMs.<\/jats:p>","DOI":"10.1145\/3713076","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T08:33:17Z","timestamp":1737534797000},"page":"1-35","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Stochastic Block Models for Complex Network Analysis: A Survey"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1790-3751","authenticated-orcid":false,"given":"Xueyan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Jilin University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineer (Jilin University), Ministry of Education, Changchun, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1607-3402","authenticated-orcid":false,"given":"Wenzhuo","family":"Song","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northeast Normal University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineer (Jilin University), Ministry of Education, Changchun, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6038-7647","authenticated-orcid":false,"given":"Katarzyna","family":"Musial","sequence":"additional","affiliation":[{"name":"Complex Adaptive Systems Lab, Data Science Institute, University of Technology Sydney, Sydney, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9642-9260","authenticated-orcid":false,"given":"Yang","family":"Li","sequence":"additional","affiliation":[{"name":"Aviation University of the Air Force, Changchun, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0003-285X","authenticated-orcid":false,"given":"Xuehua","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Digital Media, Shenzhen Institute of Information Technology, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1927-8419","authenticated-orcid":false,"given":"Bo","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Jilin University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineer (Jilin University), Ministry of Education, Changchun, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,2,22]]},"reference":[{"issue":"177","key":"e_1_3_2_2_2","first-page":"1","article-title":"Community detection and stochastic block models: Recent developments","volume":"18","author":"Abbe Emmanuel","year":"2018","unstructured":"Emmanuel Abbe. 2018. Community detection and stochastic block models: Recent developments. Journal of Machine Learning Research 18, 177 (2018), 1\u201386.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_2_3_2","unstructured":"Christopher Aicher Abigail Z. Jacobs and Aaron Clauset. 2013. Adapting the stochastic block model to edge-weighted networks. arXiv:1305.5782. Retrieved from https:\/\/arxiv.org\/abs\/1305.5782"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1093\/comnet\/cnu026"},{"issue":"9","key":"e_1_3_2_5_2","first-page":"1981","article-title":"Mixed membership stochastic blockmodels","volume":"9","author":"Airoldi Edoardo M.","year":"2008","unstructured":"Edoardo M. Airoldi, David M. Blei, Stephen E. Fienberg, and Eric C. Xing. 2008. Mixed membership stochastic blockmodels. Journal of Machine Learning Research 9, 9 (2008), 1981\u20132014.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.036103"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1173299"},{"key":"e_1_3_2_8_2","unstructured":"Albert-L\u00e1szl\u00f3 Barab\u00e1si and M\u00e1rton P\u00f3sfai. 2016. Network Science. Cambridge University Press Cambridge. Retrieved from http:\/\/barabasi.com\/networksciencebook\/"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1093\/jrsssa\/qnad007"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.03.042"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2015.07.001"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.11.050"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2016.1246365"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/PDCAT46702.2019.00102"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.11.098"},{"key":"e_1_3_2_16_2","doi-asserted-by":"crossref","first-page":"P03021","DOI":"10.1088\/1742-5468\/2014\/03\/P03021","article-title":"Overlapping community detection in networks with positive and negative links","volume":"3","author":"Chen Yi","year":"2014","unstructured":"Yi Chen, X. L. Wang, Bo Yuan, and B. Z. Tang. 2014. Overlapping community detection in networks with positive and negative links. Journal of Statistical Mechanics: Theory and Experiment 2014, 3 (2014), P03021.","journal-title":"Journal of Statistical Mechanics: Theory and Experiment"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12202"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asr053"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2020.100286"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1177\/1471082X15577017"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.02.031"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-007-9046-7"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.042317"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1177\/1471082X211033169"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1977.tb01600.x"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1002\/wics.1566"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2014.2369374"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2016.2521376"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.5555\/3454287.3455421"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1145\/1553374.1553416"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0215296"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1214\/ECP.v15-1532"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1606316113"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1561\/2200000005"},{"key":"e_1_3_2_35_2","first-page":"2249","volume-title":"25th International Conference on Neural Information Processing Systems","author":"Gopalan Prem","year":"2012","unstructured":"Prem Gopalan, David Mimno, Sean M. Gerrish, Michael J. Freedman, and David M. Blei. 2012. Scalable inference of overlapping communities. In25th International Conference on Neural Information Processing Systems, 2249\u20132257."},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1221839110"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.5555\/1051706"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1003374"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.5555\/3045118.3045279"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v31i1.10489"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v36i4.20319"},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.032819"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.100.258701"},{"key":"e_1_3_2_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/0378-8733(83)90021-7"},{"key":"e_1_3_2_45_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1981.10477598"},{"key":"e_1_3_2_46_2","first-page":"1578","volume-title":"34th International Conference on Machine Learning","author":"Hu Changwei","year":"2017","unstructured":"Changwei Hu, Piyush Rai, and Lawrence Carin. 2017. Deep generative models for relational data with side information. In 34th International Conference on Machine Learning. PMLR, 1578\u20131586."},{"key":"e_1_3_2_47_2","doi-asserted-by":"publisher","DOI":"10.5555\/2789272.2912088"},{"key":"e_1_3_2_48_2","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v33i01.33013878"},{"key":"e_1_3_2_49_2","doi-asserted-by":"publisher","DOI":"10.1145\/2043932.2043946"},{"key":"e_1_3_2_50_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.91.062805"},{"issue":"2","key":"e_1_3_2_51_2","first-page":"1149","article-title":"A survey of community detection approaches: From statistical modeling to deep learning","volume":"35","author":"Jin Di","year":"2021","unstructured":"Di Jin, Zhizhi Yu, Pengfei Jiao, Shirui Pan, Dongxiao He, Jia Wu, S. Yu Philip, and Weixiong Zhang. 2021. A survey of community detection approaches: From statistical modeling to deep learning. IEEE Transactions on Knowledge and Data Engineering 35, 2 (2021), 1149\u20131170.","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"e_1_3_2_52_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.016107"},{"key":"e_1_3_2_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.12.028"},{"key":"e_1_3_2_54_2","first-page":"381","volume-title":"21st National Conference on Artificial Intelligence","author":"Kemp Charles","year":"2006","unstructured":"Charles Kemp, Joshua B. Tenenbaum, Thomas L. Griffiths, Takeshi Yamada, and Naonori Ueda. 2006. Learning systems of concepts with an infinite relational model. In 21st National Conference on Artificial Intelligence, 381\u2013388."},{"key":"e_1_3_2_55_2","volume-title":"International Conference on Learning Representations","author":"Kipf Thomas N.","year":"2017","unstructured":"Thomas N. Kipf and Max Welling. 2017. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations. Retrieved from https:\/\/openreview.net\/forum?id=SJU4ayYgl"},{"key":"e_1_3_2_56_2","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOAS382"},{"key":"e_1_3_2_57_2","doi-asserted-by":"publisher","DOI":"10.1177\/1471082X1001200105"},{"key":"e_1_3_2_58_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41109-019-0232-2"},{"key":"e_1_3_2_59_2","first-page":"45","volume-title":"Book of the Short Papers SIS 2022","author":"Legramanti Sirio","year":"2022","unstructured":"Sirio Legramanti, Tommaso Rigon, Daniele Durante, et al. 2022. Bayesian clustering of brain regions via extended stochastic block models. In Book of the Short Papers SIS 2022. Pearson, 45\u201351."},{"key":"e_1_3_2_60_2","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOAS1595"},{"key":"e_1_3_2_61_2","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/2021.acl-long.391"},{"key":"e_1_3_2_62_2","first-page":"723","volume-title":"Artificial Intelligence and Statistics","author":"Li Wenzhe","year":"2016","unstructured":"Wenzhe Li, Sungjin Ahn, and Max Welling. 2016. Scalable MCMC for mixed membership stochastic blockmodels. In Artificial Intelligence and Statistics. PMLR, 723\u2013731."},{"key":"e_1_3_2_63_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.110068"},{"key":"e_1_3_2_64_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2017.2720180"},{"key":"e_1_3_2_65_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2023.107836"},{"key":"e_1_3_2_66_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2020.105714"},{"key":"e_1_3_2_67_2","doi-asserted-by":"publisher","DOI":"10.1145\/3442589"},{"key":"e_1_3_2_68_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11280-021-00918-y"},{"key":"e_1_3_2_69_2","doi-asserted-by":"publisher","DOI":"10.1145\/3444688"},{"key":"e_1_3_2_70_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2013.08.002"},{"key":"e_1_3_2_71_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1751645"},{"key":"e_1_3_2_72_2","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOAS361"},{"key":"e_1_3_2_73_2","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12200"},{"key":"e_1_3_2_74_2","first-page":"4466","volume-title":"36th International Conference on Machine Learning","author":"Mehta Nikhil","year":"2019","unstructured":"Nikhil Mehta, Lawrence Carin Duke, and Piyush Rai. 2019. Stochastic blockmodels meet graph neural networks. In 36th International Conference on Machine Learning. PMLR, 4466\u20134474."},{"issue":"121","key":"e_1_3_2_75_2","article-title":"The computer Science and physics of community detection: Landscapes, Phase transitions, and hardness","volume":"1","author":"Moore Cristopher","year":"2017","unstructured":"Cristopher Moore. 2017. The computer Science and physics of community detection: Landscapes, Phase transitions, and hardness. Bulletin of EATCS 1, 121 (2017).","journal-title":"Bulletin of EATCS"},{"key":"e_1_3_2_76_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0601602103"},{"key":"e_1_3_2_77_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms11863"},{"key":"e_1_3_2_78_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0610537104"},{"key":"e_1_3_2_79_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10260-021-00590-6"},{"key":"e_1_3_2_80_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2013.01.023"},{"key":"e_1_3_2_81_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2019.8683631"},{"key":"e_1_3_2_82_2","doi-asserted-by":"publisher","DOI":"10.1214\/16-EJS1211"},{"key":"e_1_3_2_83_2","first-page":"20779","article-title":"Curvature regularization to prevent distortion in graph embedding","volume":"33","author":"Pei Hongbin","year":"2020","unstructured":"Hongbin Pei, Bingzhe Wei, Kevin Chang, Chunxu Zhang, and Bo Yang. 2020. Curvature regularization to prevent distortion in graph embedding. Advances in Neural Information Processing Systems 33 (2020), 20779\u201320790.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_84_2","volume-title":"International Conference on Learning Representations","author":"Pei Hongbin","year":"2019","unstructured":"Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang. 2019. Geom-GCN: Geometric graph convolutional networks. In International Conference on Learning Representations. Retrieved from https:\/\/openreview.net\/forum?id=S1e2agrFvS"},{"key":"e_1_3_2_85_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2020.3023092"},{"key":"e_1_3_2_86_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.148701"},{"key":"e_1_3_2_87_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.5.011033"},{"key":"e_1_3_2_88_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.012306"},{"key":"e_1_3_2_89_2","doi-asserted-by":"publisher","DOI":"10.1002\/9781119483298.ch11"},{"key":"e_1_3_2_90_2","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2017\/365"},{"key":"e_1_3_2_91_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2017.2783325"},{"key":"e_1_3_2_92_2","doi-asserted-by":"publisher","DOI":"10.1002\/sta4.426"},{"key":"e_1_3_2_93_2","doi-asserted-by":"publisher","DOI":"10.1093\/comnet\/cnab032"},{"key":"e_1_3_2_94_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.96.032310"},{"key":"e_1_3_2_95_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11634-022-00492-9"},{"key":"e_1_3_2_96_2","doi-asserted-by":"publisher","DOI":"10.1002\/sam.11146"},{"key":"e_1_3_2_97_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.11.110"},{"key":"e_1_3_2_98_2","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2012.2235191"},{"key":"e_1_3_2_99_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.056111"},{"key":"e_1_3_2_100_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2021.3082932"},{"key":"e_1_3_2_101_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.soc.012809.102709"},{"key":"e_1_3_2_102_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003579900004"},{"key":"e_1_3_2_103_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2020.10.008"},{"key":"e_1_3_2_104_2","doi-asserted-by":"publisher","DOI":"10.1145\/3460231.3474238"},{"key":"e_1_3_2_105_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2018.08.072"},{"key":"e_1_3_2_106_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNSE.2016.2537545"},{"key":"e_1_3_2_107_2","doi-asserted-by":"publisher","DOI":"10.1145\/2956185"},{"key":"e_1_3_2_108_2","doi-asserted-by":"publisher","DOI":"10.1145\/2517085"},{"key":"e_1_3_2_109_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.6.011036"},{"key":"e_1_3_2_110_2","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/42.4.270"},{"key":"e_1_3_2_111_2","doi-asserted-by":"publisher","DOI":"10.5555\/1051763"},{"key":"e_1_3_2_112_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478385"},{"key":"e_1_3_2_113_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-020-2827-9"},{"key":"e_1_3_2_114_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2020.2997043"},{"key":"e_1_3_2_115_2","doi-asserted-by":"publisher","DOI":"10.1086\/226141"},{"key":"e_1_3_2_116_2","unstructured":"Christian Tobias Willenbockel and Christof Sch\u00fctte. 2016. Variational Bayesian inference and model selection for the stochastic block model with irrelevant vertices. Technical Report 16-01. ZIB Berlin."},{"key":"e_1_3_2_117_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-18579-4_30"},{"key":"e_1_3_2_118_2","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOAS311"},{"key":"e_1_3_2_119_2","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2014.2310294"},{"key":"e_1_3_2_120_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2014.67"},{"key":"e_1_3_2_121_2","doi-asserted-by":"publisher","DOI":"10.1145\/2213836.2213894"},{"key":"e_1_3_2_122_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2019.10.069"},{"key":"e_1_3_2_123_2","doi-asserted-by":"publisher","DOI":"10.1109\/tkde.2007.1061"},{"key":"e_1_3_2_124_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2016.2605085"},{"key":"e_1_3_2_125_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2011.2167751"},{"key":"e_1_3_2_126_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2017.2700304"},{"key":"e_1_3_2_127_2","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v29i1.9160"},{"key":"e_1_3_2_128_2","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v29i1.9448"},{"key":"e_1_3_2_129_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-010-5214-7"},{"key":"e_1_3_2_130_2","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.01035"},{"key":"e_1_3_2_131_2","doi-asserted-by":"publisher","DOI":"10.1145\/3350546.3352511"},{"key":"e_1_3_2_132_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2019.2960222"},{"key":"e_1_3_2_133_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2938895"},{"key":"e_1_3_2_134_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13885"},{"key":"e_1_3_2_135_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.052802"},{"key":"e_1_3_2_136_2","doi-asserted-by":"publisher","DOI":"10.3233\/FAIA200282"},{"key":"e_1_3_2_137_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2018.04.013"},{"key":"e_1_3_2_138_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.033325"}],"container-title":["ACM Transactions on Knowledge Discovery from Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3713076","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3713076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T19:58:10Z","timestamp":1772222290000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3713076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,22]]},"references-count":137,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,4,30]]}},"alternative-id":["10.1145\/3713076"],"URL":"https:\/\/doi.org\/10.1145\/3713076","relation":{},"ISSN":["1556-4681","1556-472X"],"issn-type":[{"value":"1556-4681","type":"print"},{"value":"1556-472X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,22]]},"assertion":[{"value":"2023-03-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-12-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-22","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}