{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T08:40:02Z","timestamp":1741423202041,"version":"3.38.0"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T00:00:00Z","timestamp":1734998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T00:00:00Z","timestamp":1734998400000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s40314-024-03050-5","type":"journal-article","created":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T09:46:18Z","timestamp":1735033578000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["EM algorithm for bounded generalized t mixture model with an application to image segmentation"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1121-2466","authenticated-orcid":false,"given":"Abbas","family":"Mahdavi","sequence":"first","affiliation":[]},{"given":"Narayanaswamy","family":"Balakrishnan","sequence":"additional","affiliation":[]},{"given":"Ahad","family":"Jamalizadeh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,24]]},"reference":[{"key":"3050_CR1","volume-title":"Second international symposium on information theory","author":"H Akaike","year":"1973","unstructured":"Akaike H (1973) Information theory as an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second international symposium on information theory. Academiai Kiado, BNPBF Csaki Budapest"},{"issue":"8","key":"3050_CR2","doi-asserted-by":"publisher","first-page":"1505","DOI":"10.1081\/STA-120022242","volume":"32","author":"O Arslan","year":"2003","unstructured":"Arslan O, Gen\u00e7 AI (2003) Robust location and scale estimation based on the univariate generalized t (GT) distribution. Commun Stat Theory Methods 32(8):1505\u20131525","journal-title":"Commun Stat Theory Methods"},{"issue":"1\u20132","key":"3050_CR3","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1080\/00949659208811452","volume":"44","author":"SE Atkinson","year":"1992","unstructured":"Atkinson SE (1992) The performance of standard and hybrid EM algorithms for ML estimates of the normal mixture model with censoring. J Stat Comput Simul 44(1\u20132):105\u2013115","journal-title":"J Stat Comput Simul"},{"issue":"17","key":"3050_CR4","doi-asserted-by":"publisher","first-page":"13239","DOI":"10.1007\/s00500-020-04737-7","volume":"24","author":"M Azam","year":"2020","unstructured":"Azam M, Bouguila N (2020) Multivariate bounded support Laplace mixture model. Soft Comput 24(17):13239\u201313268","journal-title":"Soft Comput"},{"issue":"2","key":"3050_CR5","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1109\/18.32132","volume":"35","author":"ZD Bai","year":"1989","unstructured":"Bai ZD, Krishnaiah PR, Zhao LC (1989) On rates of convergence of efficient detection criteria in signal processing with white noise. IEEE Trans Inf Theory 35(2):380\u2013388","journal-title":"IEEE Trans Inf Theory"},{"key":"3050_CR6","unstructured":"Bakas S, Akbari H, Sotiras A, Bilello M, Rozycki M, Kirby J, Freymann J, Farahani K, Davatzikos C (2017a) Segmentation labels and radiomic features for the pre-operative scans of the TCGA-LGG collection. Cancer Imaging Arch 286:1"},{"key":"3050_CR7","doi-asserted-by":"crossref","unstructured":"Bakas S, Akbari H, Sotiras A, Bilello M, Rozycki M, Kirby JS, Freymann JB, Farahani K, Davatzikos C (2017b) Advancing the cancer genome atlas glioma MRI collections with expert segmentation labels and radiomic features. Sci Data 4(1):1\u201313","DOI":"10.1038\/sdata.2017.117"},{"key":"3050_CR8","unstructured":"Bakas S, Reyes M, Jakab A, Bauer S, Rempfler M, Crimi A, Shinohara RT, Berger C, Ha SM, Rozycki M et\u00a0al (2018) Identifying the best machine learning algorithms for brain tumor segmentation, progression assessment, and overall survival prediction in the brats challenge. Preprint arXiv:1811.02629"},{"issue":"12","key":"3050_CR9","doi-asserted-by":"publisher","first-page":"2926","DOI":"10.1016\/j.csda.2009.09.031","volume":"54","author":"RM Basso","year":"2010","unstructured":"Basso RM, Lachos VH, Cabral CRB, Ghosh P (2010) Robust mixture modeling based on scale mixtures of skew-normal distributions. Comput Stat Data Anal 54(12):2926\u20132941","journal-title":"Comput Stat Data Anal"},{"key":"3050_CR10","doi-asserted-by":"crossref","unstructured":"Bi H, Tang H, Shu HZ, Dillenseger JL (2017) Bounded Rayleigh mixture model for ultrasound image segmentation. In: 8th international conference on graphic and image processing (ICGIP 2016), SPIE, vol 10225, pp 215\u2013219","DOI":"10.1117\/12.2266963"},{"issue":"1","key":"3050_CR11","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.csda.2011.06.026","volume":"56","author":"CRB Cabral","year":"2012","unstructured":"Cabral CRB, Lachos VH, Prates MO (2012) Multivariate mixture modeling using skew-normal independent distributions. Comput Stat Data Anal 56(1):126\u2013142","journal-title":"Comput Stat Data Anal"},{"issue":"3","key":"3050_CR12","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1080\/03610926.2018.1549243","volume":"49","author":"MN \u00c7ankaya","year":"2020","unstructured":"\u00c7ankaya MN, Arslan O (2020) On the robustness properties for maximum likelihood estimators of parameters in exponential power and generalized t distributions. Commun Stat Theory Methods 49(3):607\u2013630","journal-title":"Commun Stat Theory Methods"},{"issue":"1","key":"3050_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc Ser B (Methodol) 39(1):1\u201322","journal-title":"J Roy Stat Soc Ser B (Methodol)"},{"issue":"3","key":"3050_CR14","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/BF03263543","volume":"68","author":"C Flecher","year":"2010","unstructured":"Flecher C, Allard D, Naveau P (2010) Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data. Metron 68(3):331\u2013345","journal-title":"Metron"},{"key":"3050_CR15","doi-asserted-by":"publisher","DOI":"10.1201\/9780429055911","volume-title":"Handbook of mixture analysis","author":"S Fruhwirth-Schnatter","year":"2019","unstructured":"Fruhwirth-Schnatter S, Celeux G, Robert CP (2019) Handbook of mixture analysis. CRC Press, Boca Raton"},{"key":"3050_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-94-007-5857-5_1","volume":"214","author":"YH Han","year":"2013","unstructured":"Han YH, Park DS, Jia W, Yeo SS (2013) Ubiquitous information technologies and applications. Lect Notes Electr Eng 214:1","journal-title":"Lect Notes Electr Eng"},{"issue":"2","key":"3050_CR17","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1111\/jtsa.12224","volume":"38","author":"A Harvey","year":"2017","unstructured":"Harvey A, Lange RJ (2017) Volatility modeling with a generalized t distribution. J Time Ser Anal 38(2):175\u2013190","journal-title":"J Time Ser Anal"},{"issue":"4","key":"3050_CR18","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1109\/89.848220","volume":"8","author":"P Hedelin","year":"2000","unstructured":"Hedelin P, Skoglund J (2000) Vector quantization based on Gaussian mixture models. IEEE Trans Speech Audio Process 8(4):385\u2013401","journal-title":"IEEE Trans Speech Audio Process"},{"key":"3050_CR19","doi-asserted-by":"publisher","DOI":"10.1002\/0471725250","volume-title":"Robust statistics","author":"PJ Huber","year":"1981","unstructured":"Huber PJ (1981) Robust statistics. Wiley, New York"},{"issue":"1","key":"3050_CR20","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert L, Arabie P (1985) Comparing partitions. J Classif 2(1):193\u2013218","journal-title":"J Classif"},{"key":"3050_CR21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511550683","volume-title":"Multivariate t-distributions and their applications","author":"S Kotz","year":"2004","unstructured":"Kotz S, Nadarajah S (2004) Multivariate t-distributions and their applications. Cambridge University Press, Cambridge"},{"issue":"408","key":"3050_CR22","first-page":"881","volume":"84","author":"KL Lange","year":"1989","unstructured":"Lange KL, Little RJ, Taylor JM (1989) Robust statistical modeling using the t distribution. J Am Stat Assoc 84(408):881\u2013896","journal-title":"J Am Stat Assoc"},{"issue":"9","key":"3050_CR23","doi-asserted-by":"publisher","first-page":"2816","DOI":"10.1016\/j.csda.2012.03.003","volume":"56","author":"G Lee","year":"2012","unstructured":"Lee G, Scott C (2012) EM algorithms for multivariate Gaussian mixture models with truncated and censored data. Comput Stat Data Anal 56(9):2816\u20132829","journal-title":"Comput Stat Data Anal"},{"issue":"3","key":"3050_CR24","doi-asserted-by":"publisher","first-page":"1461","DOI":"10.1007\/s00181-018-1570-0","volume":"58","author":"R Li","year":"2020","unstructured":"Li R, Nadarajah S (2020) A review of student\u2019s t distribution and its generalizations. Empir Econ 58(3):1461\u20131490","journal-title":"Empir Econ"},{"issue":"1","key":"3050_CR25","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1109\/TSA.2002.805639","volume":"11","author":"J Lindblom","year":"2003","unstructured":"Lindblom J, Samuelsson J (2003) Bounded support Gaussian mixture modeling of speech spectra. IEEE Trans Speech Audio Process 11(1):88\u201399","journal-title":"IEEE Trans Speech Audio Process"},{"issue":"4","key":"3050_CR26","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1093\/biomet\/81.4.633","volume":"81","author":"C Liu","year":"1994","unstructured":"Liu C, Rubin DB (1994) The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika 81(4):633\u2013648","journal-title":"Biometrika"},{"key":"3050_CR27","doi-asserted-by":"crossref","unstructured":"Mahdavi A, Amirzadeh V, Jamalizadeh A, Lin TI (2021a) Maximum likelihood estimation for scale-shape mixtures of flexible generalized skew normal distributions via selection representation. Comput Stat 36:2201\u20132230","DOI":"10.1007\/s00180-021-01079-2"},{"key":"3050_CR28","doi-asserted-by":"crossref","unstructured":"Mahdavi A, Amirzadeh V, Jamalizadeh A, Lin TI (2021b) A multivariate flexible skew-symmetric-normal distribution: scale-shape mixtures and parameter estimation via selection representation. Symmetry 13(8):1343","DOI":"10.3390\/sym13081343"},{"key":"3050_CR29","doi-asserted-by":"crossref","unstructured":"Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings 8th IEEE international conference on computer vision. ICCV 2001, vol\u00a02. IEEE, pp 416\u2013423","DOI":"10.1109\/ICCV.2001.937655"},{"issue":"3","key":"3050_CR30","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1017\/S0266466600013384","volume":"4","author":"JB McDonald","year":"1988","unstructured":"McDonald JB, Newey WK (1988) Partially adaptive estimation of regression models via the generalized t distribution. Economet Theor 4(3):428\u2013457","journal-title":"Economet Theor"},{"key":"3050_CR31","doi-asserted-by":"publisher","first-page":"571","DOI":"10.2307\/2531869","volume":"1988","author":"G McLachlan","year":"1988","unstructured":"McLachlan G, Jones P (1988) Fitting mixture models to grouped and truncated data via the EM algorithm. Biometrics 1988:571\u2013578","journal-title":"Biometrics"},{"issue":"2","key":"3050_CR32","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1093\/biomet\/80.2.267","volume":"80","author":"XL Meng","year":"1993","unstructured":"Meng XL, Rubin DB (1993) Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80(2):267\u2013278","journal-title":"Biometrika"},{"issue":"10","key":"3050_CR33","doi-asserted-by":"publisher","first-page":"1993","DOI":"10.1109\/TMI.2014.2377694","volume":"34","author":"BH Menze","year":"2014","unstructured":"Menze BH, Jakab A, Bauer S, Kalpathy-Cramer J, Farahani K, Kirby J, Burren Y, Porz N, Slotboom J, Wiest R et al (2014) The multimodal brain tumor image segmentation benchmark (brats). IEEE Trans Med Imaging 34(10):1993\u20132024","journal-title":"IEEE Trans Med Imaging"},{"issue":"5","key":"3050_CR34","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1080\/02331880701747660","volume":"42","author":"S Nadarajah","year":"2008","unstructured":"Nadarajah S (2008) On the generalized t (GT) distribution. Statistics 42(5):467\u2013473","journal-title":"Statistics"},{"issue":"6","key":"3050_CR35","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1109\/TCYB.2013.2273714","volume":"44","author":"TM Nguyen","year":"2013","unstructured":"Nguyen TM, Wu QJ (2013) Bounded asymmetrical student\u2019s-t mixture model. IEEE Trans Cybern 44(6):857\u2013869","journal-title":"IEEE Trans Cybern"},{"issue":"9","key":"3050_CR36","doi-asserted-by":"publisher","first-page":"3132","DOI":"10.1016\/j.patcog.2014.03.030","volume":"47","author":"TM Nguyen","year":"2014","unstructured":"Nguyen TM, Wu QJ, Zhang H (2014) Bounded generalized Gaussian mixture model. Pattern Recogn 47(9):3132\u20133142","journal-title":"Pattern Recogn"},{"key":"3050_CR37","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1023\/A:1008981510081","volume":"10","author":"D Peel","year":"2000","unstructured":"Peel D, McLachlan GJ (2000) Robust mixture modelling using the t distribution. Stat Comput 10:339\u2013348","journal-title":"Stat Comput"},{"key":"3050_CR38","volume-title":"Robust statistics: the approach based on influence functions","author":"PJ Rousseeuw","year":"1986","unstructured":"Rousseeuw PJ, Hampel FR, Ronchetti EM, Stahel WA (1986) Robust statistics: the approach based on influence functions. Wiley, New York"},{"issue":"2","key":"3050_CR39","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461\u2013464","journal-title":"Ann Stat"},{"key":"3050_CR40","doi-asserted-by":"crossref","unstructured":"Sun J, Ji Z (2016) Bounded asymmetric Gaussian mixture model with spatial constraint for image segmentation. In: 2016 international conference on progress in informatics and computing (PIC). IEEE, pp 369\u2013373","DOI":"10.1109\/PIC.2016.7949528"},{"key":"3050_CR41","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s11042-012-1336-1","volume":"72","author":"T Xiong","year":"2014","unstructured":"Xiong T, Yi Z, Zhang L (2014) Grayscale image segmentation by spatially variant mixture model with Student\u2019s t-distribution. Multimed Tools Appl 72:167\u2013189","journal-title":"Multimed Tools Appl"},{"issue":"2","key":"3050_CR42","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/j.jeconom.2010.01.013","volume":"157","author":"D Zhu","year":"2010","unstructured":"Zhu D, Galbraith JW (2010) A generalized asymmetric student-t distribution with application to financial econometrics. J Econ 157(2):297\u2013305","journal-title":"J Econ"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-03050-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-03050-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-03050-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T07:58:53Z","timestamp":1741420733000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-03050-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,24]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["3050"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-03050-5","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2024,12,24]]},"assertion":[{"value":"22 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 December 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all the authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"89"}}