{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:31:48Z","timestamp":1777703508529,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2015,11,21]],"date-time":"2015-11-21T00:00:00Z","timestamp":1448064000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,11,27]]},"abstract":"<jats:p>\n                    The analysis of fuzzy(overlapping) community structure in complex networks is an important problem in data mining of network data sets. However, due to the exist of random factors and error edges in real networks, how to measure the significance of community structure efficiently is a crucial question. In this paper, we present a novel statistical framework comparing the significance of fuzzy community structure across various optimization models. Different from the universal approaches, we calculate the similarity between a given node and its leader and employ the distribution of link tightness to derive the significance score, instead of a direct comparison to a randomized model. Based on the distribution of community tightness, a new \u201c\n                    <jats:italic>p<\/jats:italic>\n                    -value\u201d form significance measure is proposed for community structure analysis. Specially, the well-known approaches and their corresponding quality functions are unified to a novel general formulation, which facilitate providing a detail comparison across them. To determine the position of leaders and their corresponding followers, an efficient algorithm is proposed based on the spectral theory. Finally, we apply the significance analysis to some famous benchmark networks and the good performance verified the effectiveness and efficiency of our framework.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151974","type":"journal-article","created":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T14:29:33Z","timestamp":1449671373000},"page":"2707-2715","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["The comparison of significance of fuzzy community partition across optimization methods"],"prefix":"10.1177","volume":"29","author":[{"given":"Hui-Jia","family":"Li","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,11,21]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.065701"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.066106"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.046110"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.056117"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0018961"},{"key":"e_1_3_1_7_2","first-page":"849","article-title":"On spectral clustering: Analysis and an algorithm","volume":"2","author":"Ng AY","year":"2002","unstructured":"Ng AY, Jordan MI, Weiss Y2002On spectral clustering: Analysis and an algorithmAdvances in Neural Information Processing Systems2849856","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"1","key":"e_1_3_1_8_2","first-page":"030501","article-title":"A comparison of spectral clustering algorithms","volume":"1","author":"Verma D","year":"2003","unstructured":"Verma D, Meila M2003A comparison of spectral clustering algorithmsUniversity of Washington Tech Rep UWCSE11-18030501","journal-title":"University of Washington Tech Rep UWCSE"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2009.11.002"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/108\/68009"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.91.012801"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.016109"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/103\/58002"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.72.027104"},{"issue":"3","key":"e_1_3_1_15_2","first-page":"1853","article-title":"A testing based extraction algorithm for identifying significant communities in network","volume":"8","author":"Wilson JD","year":"2013","unstructured":"Wilson JD, Wang S, Mucha PJ, Bhamidi S, Nobel AB2013A testing based extraction algorithm for identifying significant communities in networkThe Annals of Applied Statistics8318531891","journal-title":"The Annals of Applied Statistics"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.100.258701"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.016110"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.035102"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.026113"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.066133"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0610537104"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.122653799"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.026129"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.046114"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1409770111"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature03288"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.07.023"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.036106"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1086\/jar.33.4.3629752"},{"issue":"6","key":"e_1_3_1_30_2","first-page":"066106","article-title":"Measuring the significance of community structure in complex networks","volume":"82","author":"Hu Y","year":"2010","unstructured":"Hu Y, Nie Y, Yang H, Cheng J, Fan Y, Di Z2010Measuring the significance of community structure in complex networksEurophysics Letters826066106","journal-title":"Europhysics Letters"}],"container-title":["Journal of Intelligent &amp; 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