{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:21:06Z","timestamp":1740108066528,"version":"3.37.3"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["IP-2022-10-8081"],"award-info":[{"award-number":["IP-2022-10-8081"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s10044-024-01360-2","type":"journal-article","created":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T17:44:22Z","timestamp":1733507062000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A partitioning incremental algorithm using adaptive Mahalanobis fuzzy clustering and identifying the most appropriate partition"],"prefix":"10.1007","volume":"28","author":[{"given":"Rudolf","family":"Scitovski","sequence":"first","affiliation":[]},{"given":"Kristian","family":"Sabo","sequence":"additional","affiliation":[]},{"given":"Danijel","family":"Grahovac","sequence":"additional","affiliation":[]},{"given":"Francisco","family":"Mart\u00ednez-\u00c1lvarez","sequence":"additional","affiliation":[]},{"given":"Sime","family":"Ungar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,6]]},"reference":[{"key":"1360_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-024-06150-x","author":"Y Kanzawa","year":"2024","unstructured":"Kanzawa Y (2024) Parameter extension of q-divergence-based fuzzy c-means clustering. Ann Oper Res. https:\/\/doi.org\/10.1007\/s10479-024-06150-x","journal-title":"Ann Oper Res"},{"key":"1360_CR2","first-page":"102405","volume":"102","author":"WS Moola","year":"2021","unstructured":"Moola WS, Bijker W, Belgiu M, Li M (2021) Vegetable mapping using fuzzy classification of dynamic time warping distances from time series of Sentinel-1A images. Int J Appl Earth Observ Geoinf 102:102405","journal-title":"Int J Appl Earth Observ Geoinf"},{"key":"1360_CR3","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10044-024-01236-5","volume":"27","author":"KS Neetha","year":"2024","unstructured":"Neetha KS, Narayan DL (2024) Feature selection using adaptive manta ray foraging optimization for brain tumor classification. Pattern Anal Appl 27:29","journal-title":"Pattern Anal Appl"},{"key":"1360_CR4","doi-asserted-by":"publisher","first-page":"2163","DOI":"10.1007\/s40815-023-01534-w","volume":"25","author":"AK Varshney","year":"2023","unstructured":"Varshney AK, Torra V (2023) Literature review of the recent trends and applications in various fuzzy rule-based systems. Int J Fuzzy Syst 25:2163\u20132186","journal-title":"Int J Fuzzy Syst"},{"key":"1360_CR5","first-page":"105309","volume":"129","author":"Y Zeng","year":"2019","unstructured":"Zeng Y, Xu Z, He Y, Rao Y (2019) Fuzzy entropy clustering by searching local border points for the analysis of gene expression data. Knowl Based Syst 129:105309","journal-title":"Knowl Based Syst"},{"key":"1360_CR6","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.eswa.2015.12.034","volume":"51","author":"R Scitovski","year":"2016","unstructured":"Scitovski R, Vidovi\u0107 I, Bajer D (2016) A new fast fuzzy partitioning algorithm. Expert Syst Appl 51:143\u2013150","journal-title":"Expert Syst Appl"},{"key":"1360_CR7","volume-title":"Pattern recognition","author":"S Theodoridis","year":"2009","unstructured":"Theodoridis S, Koutroumbas K (2009) Pattern recognition, 4th edn. Academic Press, Burlington","edition":"4th"},{"key":"1360_CR8","doi-asserted-by":"crossref","unstructured":"Babu\u0161ka R, van der Veen PJ, Kaymak U (2002) Improved covariance estimation for Gustafson-Kessel clustering. In: IEEE international conference on fuzzy systems, pp 1081\u20131085","DOI":"10.1109\/FUZZ.2002.1006654"},{"key":"1360_CR9","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/j.ins.2017.07.005","volume":"417","author":"Y Chaomurilige","year":"2017","unstructured":"Chaomurilige Y, Miin-Shen Y (2017) Deterministic annealing Gustafson\u2013Kessel fuzzy clustering algorithm. Inf Sci 417:435\u2013453. https:\/\/doi.org\/10.1016\/j.ins.2017.07.005","journal-title":"Inf Sci"},{"key":"1360_CR10","doi-asserted-by":"crossref","unstructured":"Gustafson DE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. In: IEEE conference on decision and control, San Diego, pp\u00a0761\u2013766","DOI":"10.1109\/CDC.1978.268028"},{"key":"1360_CR11","volume-title":"Partitional clustering algorithms","author":"L Vendramin","year":"2015","unstructured":"Vendramin L, Naldi M, Campello R (2015) Fuzzy clustering algorithms and validity indices for distributed data. In: Emre M (ed) Partitional clustering algorithms. Springer"},{"key":"1360_CR12","doi-asserted-by":"publisher","first-page":"67736","DOI":"10.1109\/ACCESS.2021.3077622","volume":"9","author":"P Sinaga","year":"2021","unstructured":"Sinaga P, Hussain I, Yang MS (2021) Entropy k-means clustering with feature reduction under unknown number of clusters. IEEE Access 9:67736\u201367751. https:\/\/doi.org\/10.1109\/ACCESS.2021.3077622","journal-title":"IEEE Access"},{"key":"1360_CR13","doi-asserted-by":"publisher","first-page":"78308","DOI":"10.1109\/ACCESS.2018.2884956","volume":"6","author":"S Yang","year":"2018","unstructured":"Yang S, Chang-Chien SJ, Nataliani Y (2018) A fully-unsupervised possibilistic C-means clustering algorithm. IEEE Access 6:78308\u201378320. https:\/\/doi.org\/10.1109\/ACCESS.2018.2884956","journal-title":"IEEE Access"},{"key":"1360_CR14","doi-asserted-by":"publisher","first-page":"866","DOI":"10.1016\/j.patcog.2010.10.018","volume":"44","author":"AM Bagirov","year":"2011","unstructured":"Bagirov AM, Ugon J, Webb D (2011) Fast modified global $$k$$-means algorithm for incremental cluster construction. Patt Recogn 44:866\u2013876","journal-title":"Patt Recogn"},{"key":"1360_CR15","unstructured":"Bagirov AM, Karmitsa N, Taheri S (2020) Partitional clustering via nonsmooth optimization. Springer"},{"key":"1360_CR16","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.cageo.2013.06.010","volume":"59","author":"R Scitovski","year":"2013","unstructured":"Scitovski R, Scitovski S (2013) A fast partitioning algorithm and its application to earthquake investigation. Comput Geosci 59:124\u2013131","journal-title":"Comput Geosci"},{"key":"1360_CR17","doi-asserted-by":"publisher","first-page":"104873","DOI":"10.1016\/j.cageo.2021.104873","volume":"156","author":"A Morales-Esteban","year":"2021","unstructured":"Morales-Esteban A, Mart\u00ednez-\u00c1lvarez F, Scitovski S, Scitovski R (2021) Mahalanobis clustering for the determination of incidence-magnitude seismic parameters for the Iberian Peninsula and the Republic of Croatia. Comput Geosci 156:104873","journal-title":"Comput Geosci"},{"key":"1360_CR18","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1109\/34.85677","volume":"13","author":"L Xie","year":"1991","unstructured":"Xie L, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13:841\u2013847","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"1360_CR19","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1109\/TPAMI.1979.4766909","volume":"2","author":"D Davies","year":"1979","unstructured":"Davies D, Bouldin D (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 2:224\u2013227","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"1360_CR20","first-page":"1","volume":"3","author":"T Calinski","year":"1974","unstructured":"Calinski T, Harabasz J (1974) A dendrite method for cluster analysis. Commun Stat 3:1\u201327","journal-title":"Commun Stat"},{"key":"1360_CR21","doi-asserted-by":"publisher","first-page":"1275","DOI":"10.1016\/j.patrec.2004.11.022","volume":"26","author":"K-L Wu","year":"2005","unstructured":"Wu K-L, Yang M-S (2005) A cluster validity index for fuzzy clustering. Pattern Recogn Lett 26:1275\u20131291","journal-title":"Pattern Recogn Lett"},{"key":"1360_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-74552-3","volume-title":"Cluster analysis and applications","author":"R Scitovski","year":"2021","unstructured":"Scitovski R, Sabo K, Mart\u00ednez-\u00c1lvarez F, Ungar \u0160 (2021) Cluster analysis and applications. Springer"},{"key":"1360_CR23","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1007\/s10898-024-01372-6","volume":"89","author":"K Sabo","year":"2024","unstructured":"Sabo K, Scitovski R, Ungar \u0160, Tomljanovi\u0107 Z (2024) A method for searching for a globally optimal k-partition of higher-dimensional datasets. J Glob Optim 89:633\u2013653. https:\/\/doi.org\/10.1007\/s10898-024-01372-6","journal-title":"J Glob Optim"},{"key":"1360_CR24","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1007\/s10898-012-0020-3","volume":"57","author":"R Grbi\u0107","year":"2013","unstructured":"Grbi\u0107 R, Nyarko EK, Scitovski R (2013) A modification of the DIRECT method for Lipschitz global optimization for a symmetric function. J Glob Optim 57:1193\u20131212","journal-title":"J Glob Optim"},{"key":"1360_CR25","doi-asserted-by":"crossref","unstructured":"Paulavi\u010dius R, \u017dilinskas J (2014) Simplicial global optimization, vol X. Springer briefs in optimization. Springer, Berlin","DOI":"10.1007\/978-1-4614-9093-7"},{"key":"1360_CR26","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1007\/s10898-017-0510-4","volume":"68","author":"R Scitovski","year":"2017","unstructured":"Scitovski R (2017) A new global optimization method for a symmetric Lipschitz continuous function and application to searching for a globally optimal partition of a one-dimensional set. J Glob Optim 68:713\u2013727","journal-title":"J Glob Optim"},{"key":"1360_CR27","doi-asserted-by":"publisher","first-page":"118878","DOI":"10.1016\/j.ins.2023.03.103","volume":"644","author":"Q Chen","year":"2023","unstructured":"Chen Q, Yu WZ, Zhao XW, Nie FP, Li XL (2023) Rooted Mahalanobis distance based Gustafson\u2013Kessel fuzzy C-means. Inf Sci 644:118878","journal-title":"Inf Sci"},{"key":"1360_CR28","unstructured":"Younis KS (1999) Weighted Mahalanobis distance for hyper-ellipsoidal clustering. PhD thesis, Air Force Institute of Technology, Ohio"},{"key":"1360_CR29","volume-title":"Cluster-formation und analyse","author":"H Sp\u00e4th","year":"1983","unstructured":"Sp\u00e4th H (1983) Cluster-formation und analyse. R. Oldenburg Verlag, M\u00fcnchen"},{"key":"1360_CR30","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1137\/100802001","volume":"22","author":"Y Nestorov","year":"2012","unstructured":"Nestorov Y (2012) Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J Optim 22:341\u2013362","journal-title":"SIAM J Optim"},{"key":"1360_CR31","doi-asserted-by":"publisher","first-page":"119853","DOI":"10.1016\/j.eswa.2023.119853","volume":"222","author":"R Scitovski","year":"2023","unstructured":"Scitovski R, Sabo K, Niki\u0107 P, Majstorovi\u0107 S (2023) A new efficient method for solving the multiple ellipse detection problem. Expert Syst Appl 222:119853","journal-title":"Expert Syst Appl"},{"key":"1360_CR32","unstructured":"Weise T (2008) Global optimization algorithms. Theory and application. http:\/\/www.it-weise.de\/projects\/book.pdf"},{"key":"1360_CR33","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10898-017-0589-7","volume":"71","author":"D Lera","year":"2018","unstructured":"Lera D, Sergeyev YD (2018) GOSH: derivative-free global optimization using multi-dimensional space-filling curves. J Glob Optim 71:193\u2013211","journal-title":"J Glob Optim"},{"key":"1360_CR34","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/BF00941892","volume":"79","author":"DR Jones","year":"1993","unstructured":"Jones DR, Perttunen CD, Stuckman BE (1993) Lipschitzian optimization without the Lipschitz constant. J Optim Theory Appl 79:157\u2013181","journal-title":"J Optim Theory Appl"},{"key":"1360_CR35","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s10898-020-00952-6","volume":"79","author":"DR Jones","year":"2021","unstructured":"Jones DR, Martins JRRA (2021) The DIRECT algorithm-25 years later. J Glob Optim 79:521\u2013566","journal-title":"J Glob Optim"},{"key":"1360_CR36","doi-asserted-by":"publisher","first-page":"6179","DOI":"10.3233\/JIFS-232334","volume":"45","author":"H Zhang","year":"2023","unstructured":"Zhang H, Liu YL, Chao H (2023) Density peak clustering based on improved dung beetle optimization and Mahalanobis metric. J Intell Fuzzy Syst 45:6179\u20136191","journal-title":"J Intell Fuzzy Syst"},{"key":"1360_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ins.2023.119046","volume":"640","author":"R Scitovski","year":"2023","unstructured":"Scitovski R, Sabo K, Grahovac D, Ungar \u0160 (2023) Minimal distance index: a new clustering performance metrics. Inf Sci 640:1\u201317","journal-title":"Inf Sci"},{"key":"1360_CR38","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/978-3-642-56181-8_2","volume-title":"Classification, clustering, and data analysis. Recent advances and applications","author":"S Bodjanova","year":"2002","unstructured":"Bodjanova S (2002) Partial defuzzification of fuzzy clusters. In: Jajuga K, Sokolowski A, Bock H-H (eds) Classification, clustering, and data analysis. Recent advances and applications. Springer, pp 27\u201333"},{"key":"1360_CR39","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1109\/TFUZZ.2011.2179303","volume":"20","author":"E H\u00fcllermeier","year":"2012","unstructured":"H\u00fcllermeier E, Rifqi M, Henzgen S, Senge R (2012) Comparing fuzzy partitions: a generalization of the rand index and related measures. IEEE Trans Fuzzy Syst 20:546\u2013556","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1360_CR40","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"1360_CR41","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1016\/j.asoc.2010.05.005","volume":"11","author":"T Chaira","year":"2011","unstructured":"Chaira T (2011) A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Appl Soft Comput 11:1711\u20131717","journal-title":"Appl Soft Comput"},{"key":"1360_CR42","volume-title":"Handbook of group decision and negotiation","author":"P Ren","year":"2021","unstructured":"Ren P, Xu Z, Kacprzyk J (2021) Group decisions with intuitionistic fuzzy sets. In: Kilgour D, Eden C (eds) Handbook of group decision and negotiation. Springer"},{"key":"1360_CR43","first-page":"49","volume":"18","author":"V Atanassova","year":"2012","unstructured":"Atanassova V, Sotirov S (2012) A new formula for de-i-fuzzification of intuitionistic fuzzy sets. Not Intuit Fuzzy Sets 18:49\u201351","journal-title":"Not Intuit Fuzzy Sets"},{"key":"1360_CR44","doi-asserted-by":"publisher","first-page":"18","DOI":"10.7546\/nifs.2024.30.1.18-25","volume":"30","author":"V Patrascu","year":"2024","unstructured":"Patrascu V (2024) Two de-i-fuzzification procedures for intuitionistic fuzzy information. Not Intuit Fuzzy Sets 30:18\u201325","journal-title":"Not Intuit Fuzzy Sets"},{"issue":"9","key":"1360_CR45","doi-asserted-by":"publisher","first-page":"1753","DOI":"10.1109\/TFUZZ.2018.2889018","volume":"27","author":"T Lei","year":"2019","unstructured":"Lei T, Jia X, Zhang Y, Liu S, Meng H, Nandi AK (2019) Superpixel-based fast fuzzy c-means clustering for color image segmentation. IEEE Trans Fuzzy Syst 27(9):1753\u20131766","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1360_CR46","doi-asserted-by":"publisher","first-page":"4099","DOI":"10.1007\/s12652-019-01218-0","volume":"10","author":"U Jamil","year":"2019","unstructured":"Jamil U, Sajid Asma, Hussain Majid, Aldabbas Omer, Alam Afshan, Shafiq M Umair (2019) Melanoma segmentation using bio-medical image analysis for-smarter mobile healthcare. J Ambient Intell Humaniz Comput 10:4099\u20134120","journal-title":"J Ambient Intell Humaniz Comput"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-024-01360-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10044-024-01360-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-024-01360-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:10:18Z","timestamp":1739304618000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10044-024-01360-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,6]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["1360"],"URL":"https:\/\/doi.org\/10.1007\/s10044-024-01360-2","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"type":"print","value":"1433-7541"},{"type":"electronic","value":"1433-755X"}],"subject":[],"published":{"date-parts":[[2024,12,6]]},"assertion":[{"value":"17 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"3"}}