{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T07:48:40Z","timestamp":1648799320190},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"14","license":[{"start":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T00:00:00Z","timestamp":1573171200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T00:00:00Z","timestamp":1573171200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s00521-019-04595-x","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T18:03:00Z","timestamp":1573236180000},"page":"10609-10632","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Efficient matrixized classification learning with separated solution process"],"prefix":"10.1007","volume":"32","author":[{"given":"Zonghai","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongdong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenli","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,8]]},"reference":[{"key":"4595_CR1","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.cma.2017.03.037","volume":"320","author":"MA Bessa","year":"2017","unstructured":"Bessa MA, Bostanabad R, Liu Z, Hu A, Apley Daniel W, Brinson C, Chen W, Liu Wing Kam (2017) A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Comput Methods Appl Mech Eng 320:633\u2013667","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4","key":"4595_CR2","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.ins.2015.08.029","volume":"328","author":"F Camastra","year":"2016","unstructured":"Camastra F, Staiano A (2016) Intrinsic dimension estimation: advances and open problems. Inf Sci 328(4):26\u201341","journal-title":"Inf Sci"},{"key":"4595_CR3","doi-asserted-by":"crossref","unstructured":"C\u00e1rdenas EH, Camargo HA, T\u00fapac YJ (2016) Imbalanced datasets in the generation of fuzzy classification systems\u2014an investigation using a multiobjective evolutionary algorithm based on decomposition. In: International conference on fuzzy systems and knowledge discovery, pp 1145\u20131452","DOI":"10.1109\/FUZZ-IEEE.2016.7737859"},{"issue":"5","key":"4595_CR4","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1016\/j.patcog.2006.09.001","volume":"40","author":"S Chen","year":"2007","unstructured":"Chen S, Wang Z, Tian Y (2007) Matrix-pattern-oriented ho-kashyap classifier with regularization learning. Pattern Recognit 40(5):1533\u20131543","journal-title":"Pattern Recognit"},{"key":"4595_CR5","volume-title":"Introduction to algorithms","author":"TH Cormen","year":"2009","unstructured":"Cormen TH, Leiserson Charles E, Rivest Ronald L, Stein Clifford (2009) Introduction to algorithms, 3rd edn. The MIT Press, Cambridge","edition":"3"},{"issue":"3","key":"4595_CR6","first-page":"273","volume":"20","author":"C Cortes","year":"1995","unstructured":"Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273\u2013297","journal-title":"Mach Learn"},{"issue":"1","key":"4595_CR7","first-page":"1","volume":"7","author":"Janez Dem\u0161ar","year":"2006","unstructured":"Dem\u0161ar Janez (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7(1):1\u201330","journal-title":"J Mach Learn Res"},{"key":"4595_CR8","volume-title":"Pattern Classif","author":"RO Duda","year":"2012","unstructured":"Duda RO, Hart PE, Stork DG (2012) Pattern Classif. Wiley, Hoboken"},{"issue":"2","key":"4595_CR9","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","volume":"7","author":"RA Fisher","year":"1936","unstructured":"Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugen 7(2):179\u2013188","journal-title":"Ann Eugen"},{"key":"4595_CR10","unstructured":"Freund Y, Schapire RE (1995) A decision-theoretic generalization of on-line learning and an application to boosting. In: EuroCOLT \u201995 proceedings of the 2nd european conference on computational learning theory, pp 23\u201327"},{"issue":"4","key":"4595_CR11","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1109\/TSMCC.2011.2161285","volume":"42","author":"M Galar","year":"2014","unstructured":"Galar M, Fern\u00e1ndez A, Barrenechea E, Bustince H, Herrera F (2014) A review on ensembles for the class imbalance problem: Bagging-, boosting-, and hybrid-based approaches. IEEE Trans Syst Man Cybern Part C Appl Rev 42(4):463\u2013484","journal-title":"IEEE Trans Syst Man Cybern Part C Appl Rev"},{"key":"4595_CR12","doi-asserted-by":"crossref","unstructured":"Germain P, Lacasse A, Marchand M (2009) Pac-bayesian learning of linear classifiers. In: International conference on machine learning, pp 353\u2013360","DOI":"10.1145\/1553374.1553419"},{"issue":"3","key":"4595_CR13","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/s11704-016-5552-0","volume":"11","author":"M Gong","year":"2017","unstructured":"Gong M, Jiang X, Li H (2017) Optimization methods for regularization-based ill-posed problems: a survey and a multi-objective framework. Front Comput Sci 11(3):362\u2013391","journal-title":"Front Comput Sci"},{"key":"4595_CR14","doi-asserted-by":"crossref","DOI":"10.1002\/9781118646106","volume-title":"Imbalanced learning: foundations, algorithms, and applications","author":"H He","year":"2013","unstructured":"He H, Ma Y (2013) Imbalanced learning: foundations, algorithms, and applications. Wiley-IEEE Press, Hoboken"},{"issue":"8","key":"4595_CR15","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1109\/34.709601","volume":"20","author":"TK Ho","year":"1998","unstructured":"Ho TK (1998) The random subspace method for constructing decision forests. IEEE Trans Pattern Anal Mach Intell 20(8):832\u2013844","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"4595_CR16","volume-title":"Nonparametric statistical methods","author":"M Hollander","year":"2013","unstructured":"Hollander M, Wolfe D, Chicken E (2013) Nonparametric statistical methods. Wiley, Hoboken"},{"key":"4595_CR17","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1080\/03610928008827904","volume":"9","author":"RL Iman","year":"1980","unstructured":"Iman RL, Davenport JM (1980) Approximations of the critical region of the friedman statistic. Commun Stat 9:571\u2013595","journal-title":"Commun Stat"},{"key":"4595_CR18","doi-asserted-by":"crossref","unstructured":"Koltchinskii V, Panchenko D (2000) Rademacher processes and bounding the risk of function learning. In: High dimensional probability II. Springer, Berlin, pp 443\u2013457","DOI":"10.1007\/978-1-4612-1358-1_29"},{"key":"4595_CR19","volume-title":"Information theory and statistics","author":"S Kullback","year":"1997","unstructured":"Kullback S (1997) Information theory and statistics. Dover Publications, Mineola"},{"issue":"3","key":"4595_CR20","first-page":"273","volume":"6","author":"J Langford","year":"2005","unstructured":"Langford J (2005) Tutorial on practical prediction theory for classification. J Mach Learn Res 6(3):273\u2013306","journal-title":"J Mach Learn Res"},{"key":"4595_CR21","unstructured":"Langford J, Shawe-Taylor J (2003) PAC-Bayes and margins. In: NIPS\u201902 proceedings of the 15th international conference on neural information processing systems. MIT Press, Cambridge, MA, USA, pp 439\u2013446"},{"issue":"14","key":"4595_CR22","doi-asserted-by":"crossref","first-page":"2281","DOI":"10.1016\/S0167-8655(03)00054-0","volume":"24","author":"J Leski","year":"2003","unstructured":"Leski J (2003) Ho-kashyap classifier with generalization control. Pattern Recognit Lett 24(14):2281\u20132290","journal-title":"Pattern Recognit Lett"},{"issue":"2","key":"4595_CR23","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1109\/TSMCB.2008.2007853","volume":"39","author":"X Liu","year":"2009","unstructured":"Liu X, Wu J, Zhou ZH (2009) Exploratory undersampling for class-imbalance learning. IEEE Trans Syst Man Cybern Part B: Cybern 39(2):539\u2013550","journal-title":"IEEE Trans Syst Man Cybern Part B: Cybern"},{"issue":"1\u20133","key":"4595_CR24","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s10444-004-7634-z","volume":"25","author":"S Mukherjee","year":"2006","unstructured":"Mukherjee S, Niyogi P, Poggio T, Rifkin R (2006) Learning theory: stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization. Adv Comput Math 25(1\u20133):161\u2013193","journal-title":"Adv Comput Math"},{"key":"4595_CR25","unstructured":"Nemenyi PB (1963) Distribution-free multiple comparisons. PhD thesis, Princeton University"},{"issue":"11","key":"4595_CR26","doi-asserted-by":"crossref","first-page":"2402","DOI":"10.1109\/TCYB.2014.2372060","volume":"45","author":"WW Ng","year":"2017","unstructured":"Ng WW, Hu J, Yeung DS, Yin S, Roli F (2017) Diversified sensitivity-based undersampling for imbalance classification problems. IEEE Trans Cybern 45(11):2402\u20132412","journal-title":"IEEE Trans Cybern"},{"key":"4595_CR27","unstructured":"Sch\u00f6lkopf B, Platt J, Hofmann T (2006) Tighter Pac-Bayes bounds. In: International conference on neural information processing systems, pp 9\u201316"},{"issue":"2","key":"4595_CR28","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1162\/153244303765208377","volume":"3","author":"M Seeger","year":"2002","unstructured":"Seeger M (2002) Pac-bayesian generalisation error bounds for gaussian process classification. J Mach Learn Res 3(2):233\u2013269","journal-title":"J Mach Learn Res"},{"key":"4595_CR29","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.patcog.2016.12.030","volume":"66","author":"G Shao","year":"2017","unstructured":"Shao G, Sang N (2017) Regularized max-min linear discriminant analysis. Pattern Recognit 66:353\u2013363","journal-title":"Pattern Recognit"},{"issue":"5","key":"4595_CR30","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1016\/j.patcog.2014.11.014","volume":"48","author":"ZB Sun","year":"2015","unstructured":"Sun ZB, Song QB, Zhu XY, Sun HL, Xu BW, Zhou YM (2015) A novel ensemble method for classifying imbalanced data. Pattern Recognit 48(5):1623\u20131637","journal-title":"Pattern Recognit"},{"key":"4595_CR31","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.neunet.2019.06.003","volume":"118","author":"Z Wang","year":"2019","unstructured":"Wang Z, Cao C (2019) Cascade interpolation learning with double subspaces and confidence disturbance for imbalanced problems. Neural Netw 118:17\u201331","journal-title":"Neural Netw"},{"issue":"5","key":"4595_CR32","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1109\/TNN.2007.911744","volume":"19","author":"Z Wang","year":"2008","unstructured":"Wang Z, Chen S, Liu J, Zhang D (2008) Pattern representation in feature extraction and classifier design: matrix versus vector. IEEE Trans Neur Network 19(5):758\u2013769","journal-title":"IEEE Trans Neur Network"},{"key":"4595_CR33","first-page":"1713","volume":"7","author":"Y Yang","year":"2006","unstructured":"Yang Y, Jiang J (2006) Considering cost asymmetry in learning classifiers. J Mach Learn Res 7:1713\u20131741","journal-title":"J Mach Learn Res"},{"issue":"6","key":"4595_CR34","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1109\/TSMCC.2009.2021989","volume":"39","author":"Z Yang","year":"2009","unstructured":"Yang Z, Tang W, Shintemirov A, Wu Q (2009) Association rule miningbased dissolved gas analysis for fault diagnosis of power transformers. IEEE Trans Syst Man Cybern Part C (Appl Rev) 39(6):597\u2013610","journal-title":"IEEE Trans Syst Man Cybern Part C (Appl Rev)"},{"key":"4595_CR35","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.patcog.2017.12.017","volume":"77","author":"X Yuan","year":"2018","unstructured":"Yuan X, Xie L, Abouelenien M (2018) A regularized ensemble framework of deep learning for cancer detection from multi-class, imbalanced training data. Pattern Recognit 77:160\u2013172","journal-title":"Pattern Recognit"},{"key":"4595_CR36","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2018.2877663","author":"Z Zhu","year":"2018","unstructured":"Zhu Z, Wang Z, Li D, Zhu Y, Du W (2018) Geometric structural ensemble learning for imbalanced problems. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2018.2877663","journal-title":"IEEE Trans Cybern"},{"issue":"5","key":"4595_CR37","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1109\/JBHI.2014.2322281","volume":"18","author":"M Zieba","year":"2014","unstructured":"Zieba M (2014) Service-oriented medical system for supporting decisions with missing and imbalanced data. IEEE J Biomed Health Inf 18(5):1533\u20131540","journal-title":"IEEE J Biomed Health Inf"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-019-04595-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-019-04595-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-019-04595-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T21:07:51Z","timestamp":1611868071000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-019-04595-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,8]]},"references-count":37,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["4595"],"URL":"https:\/\/doi.org\/10.1007\/s00521-019-04595-x","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,8]]},"assertion":[{"value":"7 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors of this manuscript state that there is no conflicts of interests between this manuscript and other published works.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}