{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T08:14:02Z","timestamp":1783757642561,"version":"3.55.0"},"publisher-location":"Singapore","reference-count":28,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819228614","type":"print"},{"value":"9789819228621","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T00:00:00Z","timestamp":1783814400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T00:00:00Z","timestamp":1783814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2027]]},"DOI":"10.1007\/978-981-92-2862-1_6","type":"book-chapter","created":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T07:49:24Z","timestamp":1783756164000},"page":"64-74","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Clustering with\u00a0Ordered Pair of\u00a0Normalized Real Numbers: A Novel Framework for\u00a0Modeling Feature Relationships"],"prefix":"10.1007","author":[{"given":"Ying","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoqin","family":"Pan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,12]]},"reference":[{"key":"6_CR1","unstructured":"Arthur, D., Vassilvitskii, S.: K-means++: the advantages of careful seeding. Tech. rep. Stanford (2006)"},{"issue":"17","key":"6_CR2","doi-asserted-by":"publisher","first-page":"12267","DOI":"10.1007\/s00500-023-08232-7","volume":"27","author":"H Cui","year":"2023","unstructured":"Cui, H., Zhang, H., Zhou, L., Yang, C., Li, B., Zhao, X.: Fuzzy analytic hierarchy process with ordered pair of normalized real numbers. Soft. Comput. 27(17), 12267\u201312288 (2023)","journal-title":"Soft. Comput."},{"key":"6_CR3","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1016\/j.patcog.2011.08.012","volume":"45","author":"RC De Amorim","year":"2012","unstructured":"De Amorim, R.C., Mirkin, B.: Minkowski metric, feature weighting and anomalous cluster initializing in k-means clustering. Pattern Recognit. 45, 1061\u20131075 (2012)","journal-title":"Pattern Recognit."},{"key":"6_CR4","doi-asserted-by":"crossref","unstructured":"Dhillon, I.S., Guan, Y., Kulis, B.: Kernel k-means: spectral clustering and normalized cuts. In: Proceedings of the tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 551\u2013556 (2004)","DOI":"10.1145\/1014052.1014118"},{"key":"6_CR5","unstructured":"Drake, J., Hamerly, G.: Accelerated k-means with adaptive distance bounds. In: Proceedings of the 5th NIPS Workshop on Optimization for Machine Learning, vol.\u00a08, pp.\u00a01\u20134 (2012)"},{"key":"6_CR6","unstructured":"Elkan, C.: Using the triangle inequality to accelerate k-means. In: Proceedings of the 20th International Conference on Machine Learning (ICML-03), pp. 147\u2013153 (2003)"},{"issue":"5","key":"6_CR7","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1109\/TPAMI.2005.95","volume":"27","author":"JZ Huang","year":"2005","unstructured":"Huang, J.Z., Ng, M.K., Rong, H., Li, Z.: Automated variable weighting in k-means type clustering. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 657\u2013668 (2005)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"8","key":"6_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11227-025-07369-6","volume":"81","author":"Y Huang","year":"2025","unstructured":"Huang, Y., Zheng, Y., Pan, X., Zhou, L.: Stepwise regression algorithm based on the ordered pair of normalized real numbers framework. J. Supercomput. 81(8), 1\u201322 (2025)","journal-title":"J. Supercomput."},{"issue":"8","key":"6_CR9","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/j.patrec.2009.09.011","volume":"31","author":"AK Jain","year":"2010","unstructured":"Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern Recognit. Lett. 31(8), 651\u2013666 (2010)","journal-title":"Pattern Recognit. Lett."},{"key":"6_CR10","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1007\/978-3-642-16773-7_2","volume-title":"Advances in Soft Computing","author":"BJ Jain","year":"2010","unstructured":"Jain, B.J., Obermayer, K.: Elkan\u2019s k-means algorithm for graphs. In: Sidorov, G., Hern\u00e1ndez Aguirre, A., Reyes Garc\u00eda, C.A. (eds.) MICAI 2010. LNCS (LNAI), vol. 6438, pp. 22\u201332. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-16773-7_2"},{"key":"6_CR11","unstructured":"Karypis, M.S.G., Kumar, V., Steinbach, M.: A comparison of document clustering techniques. In: TextMining Workshop at KDD2000, pp. 428\u2013439 (2000)"},{"issue":"6","key":"6_CR12","doi-asserted-by":"crossref","first-page":"3861","DOI":"10.3390\/app13063861","volume":"13","author":"X Li","year":"2023","unstructured":"Li, X.: A robust and high-dimensional clustering algorithm based on feature weight and entropy. Appl. Sci. 13(6), 3861 (2023)","journal-title":"Appl. Sci."},{"issue":"2","key":"6_CR13","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/S0031-3203(02)00060-2","volume":"36","author":"A Likas","year":"2003","unstructured":"Likas, A., Vlassis, N., Verbeek, J.J.: The global k-means clustering algorithm. Pattern Recogn. 36(2), 451\u2013461 (2003)","journal-title":"Pattern Recogn."},{"issue":"2","key":"6_CR14","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","volume":"28","author":"S Lloyd","year":"1982","unstructured":"Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129\u2013137 (1982)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"6_CR15","unstructured":"MacQueen, J.: Multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statisticsand Probability, vol.\u00a01, pp. 281\u2013297 (1967)"},{"issue":"1","key":"6_CR16","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1109\/72.478389","volume":"7","author":"J Mao","year":"1996","unstructured":"Mao, J., Jain, A.K.: A self-organizing network for hyperellipsoidal clustering (HEC). IEEE Trans. Neural Networks 7(1), 16\u201329 (1996)","journal-title":"IEEE Trans. Neural Networks"},{"issue":"9","key":"6_CR17","doi-asserted-by":"publisher","first-page":"1455","DOI":"10.1016\/S0031-3203(99)00137-5","volume":"33","author":"U Maulik","year":"2000","unstructured":"Maulik, U., Bandyopadhyay, S.: Genetic algorithm-based clustering technique. Pattern Recogn. 33(9), 1455\u20131465 (2000)","journal-title":"Pattern Recogn."},{"key":"6_CR18","doi-asserted-by":"crossref","unstructured":"Van\u00a0der Merwe, D., Engelbrecht, A.P.: Data clustering using particle swarm optimization. In: The 2003 Congress on Evolutionary Computation, 2003. CEC\u201903, vol.\u00a01, pp. 215\u2013220. IEEE (2003)","DOI":"10.1109\/CEC.2003.1299577"},{"key":"6_CR19","unstructured":"Minkowski, H.: Geometrie der Zahlen, vol. 1. Teubner (1910)"},{"key":"6_CR20","unstructured":"Nelson, J.D.: On k-means clustering using Mahalanobis distance. Master's thesis, North Dakota State University (2012)"},{"key":"6_CR21","unstructured":"Nguyen, T., Chaturvedi, A., Nguyen, H.L.: Improved learning-augmented algorithms for k-means and k-medians clustering. arXiv preprint arXiv:2210.17028 (2023)"},{"issue":"10","key":"6_CR22","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1016\/0031-3203(91)90097-O","volume":"24","author":"SZ Selim","year":"1991","unstructured":"Selim, S.Z., Alsultan, K.: A simulated annealing algorithm for the clustering problem. Pattern Recogn. 24(10), 1003\u20131008 (1991)","journal-title":"Pattern Recogn."},{"issue":"3","key":"6_CR23","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1038\/10343","volume":"22","author":"S Tavazoie","year":"1999","unstructured":"Tavazoie, S., Hughes, J.D., Campbell, M.J., Cho, R.J., Church, G.M.: Systematic determination of genetic network architecture. Nat. Genet. 22(3), 281\u2013285 (1999)","journal-title":"Nat. Genet."},{"key":"6_CR24","doi-asserted-by":"crossref","unstructured":"Visalakshi, N.K., Suguna, J.: K-means clustering using max-min distance measure. In: NAFIPS 2009-2009 Annual Meeting of the North American Fuzzy Information Processing Society, pp.\u00a01\u20136 (2009)","DOI":"10.1109\/NAFIPS.2009.5156398"},{"key":"6_CR25","doi-asserted-by":"crossref","unstructured":"Zhao, X., Zheng, Y., Pan, X., Zhou, L.: PCA dimensionality reduction algorithm based on ordered pair of normalized real numbers. In: Proceedings of the 17th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), pp.\u00a01\u20137 (2024)","DOI":"10.1109\/CISP-BMEI64163.2024.10906273"},{"key":"6_CR26","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Ding, X., Zhao, X., Pan, X., Zhou, L.: K-nearest neighbor algorithm based on the framework of ordered pair of normalized real numbers. IEEE Trans. Artif. Intell. (2025)","DOI":"10.1109\/TAI.2025.3566925"},{"key":"6_CR27","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.ins.2020.05.036","volume":"538","author":"L Zhou","year":"2020","unstructured":"Zhou, L.: Ordered pair of normalized real numbers. Inf. Sci. 538, 290\u2013313 (2020)","journal-title":"Inf. Sci."},{"issue":"5","key":"6_CR28","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1007\/s40745-022-00428-2","volume":"11","author":"M Zubair","year":"2024","unstructured":"Zubair, M., Iqbal, M.D.A., Shil, A., Chowdhury, M.J.M., Moni, M.A., Sarker, I.H.: An improved k-means clustering algorithm towards an efficient data-driven modeling. Ann. Data Sci. 11(5), 1525\u20131544 (2024)","journal-title":"Ann. Data Sci."}],"container-title":["Lecture Notes in Computer Science","Knowledge Science, Engineering and Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-92-2862-1_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T07:49:26Z","timestamp":1783756166000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-92-2862-1_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,12]]},"ISBN":["9789819228614","9789819228621"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-981-92-2862-1_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,12]]},"assertion":[{"value":"12 July 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"KSEM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Knowledge Science, Engineering and Management","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Beijing","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 July 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 July 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ksem2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ksem2026.rosc.org.cn\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}