{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T05:22:42Z","timestamp":1761110562712},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T00:00:00Z","timestamp":1591660800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T00:00:00Z","timestamp":1591660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Prog Artif Intell"],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s13748-020-00209-z","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T06:23:03Z","timestamp":1591683783000},"page":"221-238","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Gabriel graph-based connectivity and density for internal validity of clustering"],"prefix":"10.1007","volume":"9","author":[{"given":"Fatima","family":"Boudane","sequence":"first","affiliation":[]},{"given":"Ali","family":"Berrichi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,9]]},"reference":[{"key":"209_CR1","doi-asserted-by":"crossref","DOI":"10.1201\/9781420034912","volume-title":"Clustering for Data Mining: A Data Recovery Approach","author":"B Mirkin","year":"2005","unstructured":"Mirkin, B.: Clustering for Data Mining: A Data Recovery Approach. Chapman & Hall\/CRC, Boca Raton, Florida (2005)"},{"key":"209_CR2","volume-title":"Numerical Taxonomy. Books in Biology","author":"PHA Sneath","year":"1973","unstructured":"Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy. Books in Biology. W.H. Freeman and Company, San Francisco (1973)"},{"key":"209_CR3","first-page":"205","volume":"7","author":"CH Chou","year":"2004","unstructured":"Chou, C.H., Su, M.C., Lai, E.: A new cluster validity measure and its application to image compression. Pattern Anal. Appl. 7, 205\u2013220 (2004)","journal-title":"Pattern Anal. Appl."},{"key":"209_CR4","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/978-1-4615-0953-0","volume-title":"Applications of Data Mining in Computer Security","author":"D Barbar\u00e0","year":"2002","unstructured":"Barbar\u00e0, D., Jajodia, S.: Applications of Data Mining in Computer Security, pp. 78\u201399. Kluwer Academic Publishers, Boston, MA (2002)"},{"key":"209_CR5","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1016\/j.patrec.2012.11.009","volume":"34","author":"TH Sarma","year":"2013","unstructured":"Sarma, T.H., Viswanath, P., Reddy, B.E.: Speeding-up the kernel K-means clustering method: a prototype based hybrid approach. Pattern Recogn. Lett. 34, 564\u2013573 (2013)","journal-title":"Pattern Recogn. Lett."},{"key":"209_CR6","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2307\/2346830","volume":"28","author":"JA Hartigan","year":"1979","unstructured":"Hartigan, J.A., Wong, M.A.: A K-Means clustering algorithm. Appl. Stat. 28, 100\u2013108 (1979)","journal-title":"Appl. Stat."},{"issue":"3","key":"209_CR7","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1145\/601858.601862","volume":"31","author":"M Halkidi","year":"2002","unstructured":"Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Clustering validity checking methods: part II. Newslett. ACM SIG MOD Record. 31(3), 19\u201327 (2002). https:\/\/doi.org\/10.1145\/601858.601862","journal-title":"Newslett. ACM SIG MOD Record."},{"issue":"336","key":"209_CR8","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1080\/01621459.1971.10482356","volume":"66","author":"WM Rand","year":"1971","unstructured":"Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66(336), 846\u2013850 (1971)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"209_CR9","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193\u2013218 (1985)","journal-title":"J. Classif."},{"key":"209_CR10","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.patcog.2012.07.021","volume":"46","author":"O Arbelaitz","year":"2013","unstructured":"Arbelaitz, O., Gurrutxaga, I., Muguerza, J., P\u00e9rez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recognit. 46, 243\u2013256 (2013)","journal-title":"Pattern Recognit."},{"key":"209_CR11","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF01202268","volume":"12","author":"V Batagelj","year":"1995","unstructured":"Batagelj, V., Bren, M.: Comparing resemblance measure. J. Classif. 12, 73\u201390 (1995)","journal-title":"J. Classif."},{"issue":"3","key":"209_CR12","doi-asserted-by":"crossref","first-page":"982","DOI":"10.1109\/TSMCB.2012.2220543","volume":"43","author":"Y Liu","year":"2013","unstructured":"Liu, Y., Li, Z., Xiong, H., Gao, X., Wu, J., Wu, S.: Understanding and enhancement of internal clustering validation measures. IEEE Trans. Cybern. 43(3), 982\u2013994 (2013)","journal-title":"IEEE Trans. Cybern."},{"key":"209_CR13","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.asoc.2018.06.033","volume":"71","author":"S Zhou","year":"2018","unstructured":"Zhou, S., Xu, Z.: A novel internal validity index based on the cluster centre and the nearest neighbor cluster. Appl. Soft Comput. J. 71, 78\u201388 (2018). https:\/\/doi.org\/10.1016\/j.asoc.2018.06.033","journal-title":"Appl. Soft Comput. J."},{"issue":"1","key":"209_CR14","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/01969727408546059","volume":"4","author":"JC Dunn","year":"1974","unstructured":"Dunn, J.C.: Well separated clusters and optimal fuzzy partitions. J. Cybern. 4(1), 95\u2013104 (1974)","journal-title":"J. Cybern."},{"key":"209_CR15","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/TPAMI.1979.4766909","volume":"1","author":"DL Davies","year":"1979","unstructured":"Davies, D.L., Bouldin, D.W.: A clustering separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 1, 224\u2013227 (1979)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"209_CR16","first-page":"1","volume":"3","author":"T Calinski","year":"1974","unstructured":"Calinski, T., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat. 3, 1\u201327 (1974)","journal-title":"Commun. Stat."},{"issue":"2","key":"209_CR17","first-page":"101","volume":"8","author":"Y Lee","year":"2009","unstructured":"Lee, Y., Lee, J.H., Jun, C.H.: Validation measures of bi cluster solutions. Ind. Eng. Manag. Syst. 8(2), 101\u2013108 (2009)","journal-title":"Ind. Eng. Manag. Syst."},{"key":"209_CR18","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.patrec.2018.08.005","volume":"112","author":"S Lee","year":"2018","unstructured":"Lee, S., Jeong, Y., Kim, J., Jeong, M.K.: A new clustering validity index for arbitrary shape of clusters. Pattern Recognit. Lett. 112, 263\u2013269 (2018). https:\/\/doi.org\/10.1016\/j.patrec.2018.08.005","journal-title":"Pattern Recognit. Lett."},{"key":"209_CR19","doi-asserted-by":"crossref","unstructured":"Moulavi, D., Jaskowiak, P.A., Campello, R.J.G.B., Zimek, A., Sander, J.: Density-based clustering validation. In: Proceedings of the 14th SIAM International Conference on Data Mining (SDM), Philadelphia, PA (2014)","DOI":"10.1137\/1.9781611973440.96"},{"issue":"3","key":"209_CR20","doi-asserted-by":"crossref","first-page":"259","DOI":"10.2307\/2412323","volume":"18","author":"KR Gabriel","year":"1969","unstructured":"Gabriel, K.R., Sokal, R.R.: New statistical approach to geographic variation analysis. Syst. Zool. 18(3), 259\u2013278 (1969)","journal-title":"Syst. Zool."},{"key":"209_CR21","doi-asserted-by":"crossref","unstructured":"Zhou, S., Zhao, Y., Guan, J., Huang, J.: NBC: A neighborhood-based clustering algorithm. In: Proceedings of the 9th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), pp. 361\u2013371. (2005)","DOI":"10.1007\/11430919_43"},{"issue":"2\/3","key":"209_CR22","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1012801612483","volume":"17","author":"M Halkidi","year":"2001","unstructured":"Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inf. Syst. 17(2\/3), 107\u2013145 (2001)","journal-title":"J. Intell. Inf. Syst."},{"key":"209_CR23","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","volume":"20","author":"P Rousseeuw","year":"1987","unstructured":"Rousseeuw, P.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53\u201365 (1987)","journal-title":"J. Comput. Appl. Math."},{"key":"209_CR24","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.fss.2013.12.013","volume":"253","author":"D Zhang","year":"2014","unstructured":"Zhang, D., Ji, M., Yang, J., Zhang, Y., Xie, F.: A novel cluster validity index for fuzzy clustering based on bipartite modularity. Fuzzy Sets Syst. 253, 122\u2013137 (2014)","journal-title":"Fuzzy Sets Syst."},{"issue":"3","key":"209_CR25","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s11063-006-9005-x","volume":"23","author":"X Yang","year":"2006","unstructured":"Yang, X., Song, Q., Cao, A.: A new cluster validity for data clustering. Neural Process. Lett. 23(3), 325\u2013344 (2006)","journal-title":"Neural Process. Lett."},{"key":"209_CR26","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.eswa.2017.06.003","volume":"86","author":"JC Rojas-Thomas","year":"2017","unstructured":"Rojas-Thomas, J.C., Santos, M., Mora, M.: New internal index for clustering validation based on graphs. Expert Syst. Appl. 86, 334\u2013349 (2017)","journal-title":"Expert Syst. Appl."},{"key":"209_CR27","unstructured":"Yang, J., Lee, I.: Cluster validity through graph based boundary analysis. In: IKE, pp. 204\u2013210. (2004)"},{"issue":"6","key":"209_CR28","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/S0031-3203(96)00127-6","volume":"30","author":"N Pal","year":"1997","unstructured":"Pal, N., Biswas, J.: Cluster validation using graph theoretic concepts. Pattern Recognit. 30(6), 847\u2013857 (1997)","journal-title":"Pattern Recognit."},{"key":"209_CR29","unstructured":"Halkidi, M., Vazirgiannis, M.: Clustering validity assessment: finding the optimal partitioning of a data set. In: Proceedings of the First IEEE International Conference on Data Mining (ICDM\u201901), pp. 187\u2013194, California, USA (2001)"},{"key":"209_CR30","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.patrec.2007.12.011","volume":"29","author":"M Halkidi","year":"2008","unstructured":"Halkidi, M., Vazirgiannis, M.: A density-based cluster validity approach using multi-representatives. Pattern Recognit. Lett. 29, 773\u2013786 (2008)","journal-title":"Pattern Recognit. Lett."},{"key":"209_CR31","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.patrec.2010.08.007","volume":"32","author":"KR \u017dalik","year":"2011","unstructured":"\u017dalik, K.R., \u017dalik, B.: Validity index for clusters of different sizes and densities. Pattern Recognit. Lett. 32, 221\u2013234 (2011)","journal-title":"Pattern Recognit. Lett."},{"issue":"19","key":"209_CR32","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1093\/bioinformatics\/btl406","volume":"22","author":"A Thalamuthu","year":"2006","unstructured":"Thalamuthu, A., Mukhopadhyay, I., Zheng, X., Tseng, G.: Evaluation and comparison of gene clustering methods in microarray analysis. Bioinformatics 22(19), 2405\u20132412 (2006)","journal-title":"Bioinformatics"},{"key":"209_CR33","doi-asserted-by":"crossref","unstructured":"Carpineto, C., Romano, G.: Consensus clustering based on a new probabilistic rand index with application to subtopic retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 34, 2315\u20132326 (2012)","DOI":"10.1109\/TPAMI.2012.80"},{"key":"209_CR34","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.asoc.2017.03.030","volume":"57","author":"CC Yeh","year":"2017","unstructured":"Yeh, C.C., Yang, M.S.: Evaluation measures for cluster ensembles based on a fuzzy generalized Rand index. Appl. Soft Comput. 57, 225\u2013234 (2017)","journal-title":"Appl. Soft Comput."},{"key":"209_CR35","doi-asserted-by":"crossref","unstructured":"Zaidi, F., Melan\u00e7on, G.: Evaluating the quality of clustering algorithms using cluster path lengths, 10th Industrial Conference (ICDM), pp. 42\u201356, Berlin, Germany (2010)","DOI":"10.1007\/978-3-642-14400-4_4"},{"issue":"3","key":"209_CR36","first-page":"378","volume":"3","author":"H Almeida","year":"2012","unstructured":"Almeida, H., NetoZaki Jr., D.G.W.M.M.J.: Towards a better quality metric for graph cluster evaluation. J. Inf. Data Manag. 3(3), 378\u2013393 (2012)","journal-title":"J. Inf. Data Manag."},{"issue":"3","key":"209_CR37","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0031-3203(82)90069-3","volume":"15","author":"R Urquhart","year":"1982","unstructured":"Urquhart, R.: Graph theoretical clustering based on limited neighbourhood sets. Pattern Recognit. 15(3), 173\u2013187 (1982)","journal-title":"Pattern Recognit."},{"key":"209_CR38","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1109\/TC.1976.1674719","volume":"25","author":"WLG Koontz","year":"1976","unstructured":"Koontz, W.L.G., Narendra, P.M., Fukunaga, K.: A graph-theoretic approach to non parametric cluster analysis. IEEE Trans. Comput. 25, 936\u2013944 (1976)","journal-title":"IEEE Trans. Comput."},{"key":"209_CR39","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1016\/j.patrec.2008.01.028","volume":"29","author":"D Liu","year":"2008","unstructured":"Liu, D., Novovskiy, G.V., Sourina, O.: Effective clustering and boundary detection algorithm based on Delaunay triangulation. Pattern Recognit. Lett. 29, 1261\u20131273 (2008)","journal-title":"Pattern Recognit. Lett."},{"issue":"2","key":"209_CR40","first-page":"117","volume":"5","author":"T Inkaya","year":"2010","unstructured":"Inkaya, T., Kayal\u0131gil, S., \u00d6zdemirel, N.E.: A new density-based clustering approach in graph theoretic context. Int. J. Comput. Sci. Inf. Technol. 5(2), 117\u2013135 (2010)","journal-title":"Int. J. Comput. Sci. Inf. Technol."},{"key":"209_CR41","unstructured":"UCI machine learning repository, https:\/\/archive.ics.uci.edu\/ml\/ (2018)"},{"key":"209_CR42","volume-title":"Speech and image processing unit, clustering datasets","author":"P Franti","year":"2015","unstructured":"Franti, P.: Speech and image processing unit, clustering datasets. University of Eastern Finland, School of Computing (2015)"},{"key":"209_CR43","unstructured":"Ester, M., Kriegel, H. P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of KDD, pp. 226\u2013231 (1996)"},{"key":"209_CR44","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1016\/j.asoc.2018.07.026","volume":"71","author":"E Zhu","year":"2018","unstructured":"Zhu, E., Ma, R.: An effective partitional clustering algorithm based on new clustering validity index. Appl. Soft Comput. 71, 608\u2013621 (2018)","journal-title":"Appl. Soft Comput."},{"issue":"8","key":"209_CR45","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1109\/TKDE.2016.2551240","volume":"28","author":"M Rezaei","year":"2016","unstructured":"Rezaei, M., Fr\u00e4nti, P.: Set matching measures for external cluster validity. IEEE Trans. Knowl. Data Eng. 28(8), 2173\u20132186 (2016)","journal-title":"IEEE Trans. Knowl. Data Eng."}],"container-title":["Progress in Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13748-020-00209-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13748-020-00209-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13748-020-00209-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T23:29:32Z","timestamp":1623194972000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13748-020-00209-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,9]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["209"],"URL":"https:\/\/doi.org\/10.1007\/s13748-020-00209-z","relation":{},"ISSN":["2192-6352","2192-6360"],"issn-type":[{"value":"2192-6352","type":"print"},{"value":"2192-6360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,9]]},"assertion":[{"value":"9 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}