{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T02:54:11Z","timestamp":1768532051882,"version":"3.49.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61806219"],"award-info":[{"award-number":["61806219"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61703426"],"award-info":[{"award-number":["61703426"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61876189"],"award-info":[{"award-number":["61876189"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young Talent fund of University and Association for Science and Technology in Shaanxi, China","award":["20190108"],"award-info":[{"award-number":["20190108"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>When training base classifier by ternary Error Correcting Output Codes (ECOC), it is well know that some classes are ignored. On this account, a non-competent classifier emerges when it classify an instance whose real label does not belong to the meta-subclasses. Meanwhile, the classic ECOC dichotomizers can only produce binary outputs and have no capability of rejection for classification. To overcome the non-competence problem and better model the multi-class problem for reducing the classification cost, we embed reject option to ECOC and present a new variant of ECOC algorithm called as Reject-Option-based Re-encoding ECOC (ROECOC). The cost-sensitive classification model and cost-loss function based on Receiver Operating Characteristic (ROC) curve are built respectively. The optimal reject threshold values are obtained by combing the condition to be met for minimizing the loss function and the ROC convex hull. In so doing, reject option (<jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>t<\/jats:italic><jats:sub>2<\/jats:sub>) provides a three-symbol output to make dichotomizers more competent and ROECOC more universal and practical for cost-sensitive classification issue. Experimental results on two kinds of datasets show that our scheme with low-degree freedom of initialized ECOC can effectively enhance accuracy and reduce cost.<\/jats:p>","DOI":"10.1007\/s10489-020-01642-2","type":"journal-article","created":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T22:03:33Z","timestamp":1588370613000},"page":"3090-3100","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A new re-encoding ECOC using reject option"],"prefix":"10.1007","volume":"50","author":[{"given":"Lei","family":"Lei","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0962-0671","authenticated-orcid":false,"given":"Yafei","family":"Song","sequence":"additional","affiliation":[]},{"given":"Xi","family":"Luo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,5,1]]},"reference":[{"key":"1642_CR1","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/s10489-014-0596-z","volume":"42","author":"Y Song","year":"2015","unstructured":"Song Y, Wang X, Lei L, Xue A (2015) A novel similarity measure on intuitionistic fuzzy sets with its applications. Appl Intell 42:252\u2013261. https:\/\/doi.org\/10.1007\/s10489-014-0596-z","journal-title":"Appl Intell"},{"key":"1642_CR2","doi-asserted-by":"publisher","first-page":"1672","DOI":"10.1007\/s10489-017-1024-y","volume":"48","author":"X Wang","year":"2018","unstructured":"Wang X, Song Y (2018) Uncertainty measure in evidence theory with its applications. Appl Intell 48:1672\u20131688. https:\/\/doi.org\/10.1007\/s10489-017-1024-y","journal-title":"Appl Intell"},{"key":"1642_CR3","doi-asserted-by":"publisher","first-page":"1985","DOI":"10.1007\/s00500-017-2912-0","volume":"23","author":"Y Song","year":"2019","unstructured":"Song Y, Wang X, Quan W, Huang W (2019) A new approach to construct similarity measure for intuitionistic fuzzy sets. Soft Comput 23:1985\u20131998. https:\/\/doi.org\/10.1007\/s00500-017-2912-0","journal-title":"Soft Comput"},{"key":"1642_CR4","doi-asserted-by":"publisher","first-page":"3950","DOI":"10.1007\/s10489-018-1188-0s","volume":"48","author":"Y Song","year":"2018","unstructured":"Song Y, Wang X, Zhu J, Lei L (2018) Sensor dynamic reliability evaluation based on evidence and intuitionistic fuzzy sets. Appl Intell 48:3950\u20133962. https:\/\/doi.org\/10.1007\/s10489-018-1188-0s","journal-title":"Appl Intell"},{"issue":"105","key":"1642_CR5","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1016\/j.asoc.2019.105703","volume":"84","author":"Y Song","year":"2019","unstructured":"Song Y, Fu Q, Wang Y-F, Wang X (2019) Divergence-based cross entropy and uncertainty measures of Atanassov\u2019s intuitionistic fuzzy sets with their application in decision making. Appl Soft Comput 84(105):703. https:\/\/doi.org\/10.1016\/j.asoc.2019.105703","journal-title":"Appl Soft Comput"},{"key":"1642_CR6","doi-asserted-by":"crossref","unstructured":"T. G. Dietterich and G. Bakiri. Solving. Multi-class learning problems via error-correcting output codes. J Artif Intell Res, 1995, 34(2):263\u2013286.","DOI":"10.1613\/jair.105"},{"issue":"6","key":"1642_CR7","first-page":"25377","volume":"99","author":"P Olusegun","year":"2018","unstructured":"Olusegun P, Anastasios D et al (2018) Spatio-temporal spectrum sensing in cognitive radio networks using beamformer-aided SVM algorithms. IEEE Access 99(6):25377\u201325,388","journal-title":"IEEE Access"},{"issue":"3","key":"1642_CR8","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1109\/TCYB.2017.2785621","volume":"49","author":"C Ma","year":"2019","unstructured":"Ma C, Tsang IW, Shen F et al (2019) Error correcting input and output hashing. IEEE Transactions on Cybernetics 49(3):781\u2013791","journal-title":"IEEE Transactions on Cybernetics"},{"issue":"2","key":"1642_CR9","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/s10844-018-0516-5","volume":"52","author":"KK Zhao","year":"2019","unstructured":"Zhao KK, Matsukawa T, Suzuki E (2019) Experimental validation for N-ary error correcting output codes for ensemble learning of deep neural networks. J Intell Inf Syst 52(2):367\u2013392","journal-title":"J Intell Inf Syst"},{"issue":"1","key":"1642_CR10","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.ins.2016.02.028","volume":"349","author":"KH Liu","year":"2016","unstructured":"Liu KH, Zeng ZH, Vincent TY (2016) A hierarchical ensemble of ECOC for cancer classification based on multi-class microarray data. Inf Sci 349(1):102\u2013118","journal-title":"Inf Sci"},{"key":"1642_CR11","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1007\/s11424-017-6232-3","volume":"31","author":"XD Gu","year":"2018","unstructured":"Gu XD, Deng F, Gao X, Zhou R (2018) An improved sensor fault diagnosis scheme based on TA-LSSVM and ECOC-SVM. J Syst Sci Complex 31:372\u2013384","journal-title":"J Syst Sci Complex"},{"key":"1642_CR12","unstructured":"Crammer K, Singer Y (2000) On the learnability and design of output codes for multi-class problems. In Proc. 13th Annual Conference on Computational Learning Theory, Kluwer Academic Publishers, Boston, pp. 896\u2013909"},{"issue":"6","key":"1642_CR13","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1109\/TPAMI.2006.116","volume":"28","author":"O Pujol","year":"2006","unstructured":"Pujol O, Radeva P, Vitria J (2006) Discriminate ECOC: A heuristic method for application dependent design of error correcting output codes. IEEE Trans on Pattern Analysis and Machine Intelligence 28(6):1001\u20131007","journal-title":"IEEE Trans on Pattern Analysis and Machine Intelligence"},{"issue":"6","key":"1642_CR14","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1109\/TPAMI.2008.38","volume":"30","author":"S Escalera","year":"2008","unstructured":"Escalera S, Tax DMJ, Pujol O, Radeva P, Duin R (2008) Subclass Problem-Dependent Design for Error-Correcting Output Codes. IEEE Trans on Pattern Analysis and Machine Intelligence 30(6):1041\u20131054","journal-title":"IEEE Trans on Pattern Analysis and Machine Intelligence"},{"issue":"4","key":"1642_CR15","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/978-3-642-21738-8_11","volume":"6792","author":"D Bouzas","year":"2011","unstructured":"Bouzas D, Arvanitopoulos N, Tefas A (2011) Optimizing Linear Discriminant Error Correcting Output Codes Using Particle Swarm Optimization. Lect Notes Comput Sci 6792(4):79\u201386","journal-title":"Lect Notes Comput Sci"},{"issue":"1","key":"1642_CR16","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s10044-015-0455-5","volume":"19","author":"L Lei","year":"2016","unstructured":"Lei L, Wang XD, Luo X, Song YF (2016) Hierarchical Error-correcting Output Codes based on SVDD. Pattern Anal Applic 19(1):163\u2013171","journal-title":"Pattern Anal Applic"},{"issue":"complete","key":"1642_CR17","first-page":"158","volume":"89","author":"Y Wang","year":"2012","unstructured":"Wang Y, Chen S, Xue H (2012) Can under-exploited structure of original-classes help ECOC-based multi-class classification. Eeurocomputing 89(complete):158\u2013167","journal-title":"Eeurocomputing"},{"issue":"5","key":"1642_CR18","first-page":"555","volume":"31","author":"S Escalera","year":"2013","unstructured":"Escalera S, Pujol O (2013) Recoding ECOCs without Retraining. Pattern Recogn Lett 31(5):555\u2013562","journal-title":"Pattern Recogn Lett"},{"issue":"1","key":"1642_CR19","first-page":"012107:1","volume":"51","author":"JD Zhou","year":"2016","unstructured":"Zhou JD, Yang Y, Zhang MJ, Xing HB, Xing H (2016) Constructing ECOC based on Confusion Matrix for Multi-class Learning Problems. Science China Inf Sci 51(1):012107:1","journal-title":"Science China Inf Sci"},{"key":"1642_CR20","unstructured":"Zhong TY, Liu KH, Wang BZ (2017) Multiclass microarray data classification based on SA-ECOC. 10th International Symposium on Computational Intelligence and Design, IEEE"},{"issue":"2","key":"1642_CR21","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1109\/TNNLS.2013.2274735","volume":"25","author":"A Rocha","year":"2014","unstructured":"Rocha A, Goldenstein SK (2014) Multiclass from Bianry: Expanding one-versus-all, one-versus-one and ECOC-based approaches. IEEE Transactions on Neural Networks and Learning Systems 25(2):289\u2013302","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"1642_CR22","volume-title":"A new ECOC algorithm for multiclass microarray data classification","author":"MX Sum","year":"2018","unstructured":"Sum MX, Liu KH, Hong QQ, Wang BZ (2018) A new ECOC algorithm for multiclass microarray data classification. 24th International Conference on Pattern Recognition, Beijing"},{"key":"1642_CR23","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.engappai.2018.04.019","volume":"73","author":"L Marie","year":"2018","unstructured":"Marie L, Hegarat-Mascle SL, Aldea E (2018) Evidential framework for Error Correcting Output Codes classification. Eng Appl Artif Intell 73:10\u201321","journal-title":"Eng Appl Artif Intell"},{"issue":"1","key":"1642_CR24","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.patcog.2014.07.023","volume":"48","author":"M Galar","year":"2015","unstructured":"Galar M, Fernandez A, Barrenechea E (2015) DRCW-OVO: Distance-based relative competence weighting combination for one-vs-one strategy in multi-class problems. Pattern Recogn 48(1):28\u201342","journal-title":"Pattern Recogn"},{"issue":"3","key":"1642_CR25","first-page":"1","volume":"99","author":"M Ohsaki","year":"2017","unstructured":"Ohsaki M, Wang P, Matsuda K (2017) Confusion-matrix-based kernel logistic regression for imbalanced data classification. IEEE Trans Knowl Data Eng 99(3):1\u201310","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"1642_CR26","unstructured":"Allwein E, Schapire R, Singer Y (2000) Reducing multiclass to binary: A unifying approach for margin classifiers. In Machine Learning: Proceedings of the Seventeenth International Conference, pp. 1545\u20131550"},{"issue":"2","key":"1642_CR27","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.patrec.2004.09.004","volume":"26","author":"F Tortorella","year":"2005","unstructured":"Tortorella F (2005) A roc-based reject rule for dichotomizers. Pattern Recogn Lett 26(2):167\u2013180","journal-title":"Pattern Recogn Lett"},{"key":"1642_CR28","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.patcog.2015.10.010","volume":"46","author":"S Benard","year":"2016","unstructured":"Benard S, Chatelain C, Adam S, Saborin R (2016) The multi-class roc front method for cost-sensitive classification. Pattern Recogn 46:46\u201360","journal-title":"Pattern Recogn"},{"issue":"4","key":"1642_CR29","first-page":"132","volume":"52","author":"ZC Zhao","year":"2018","unstructured":"Zhao ZC, Wang XD (2018) A minimum risk recognition method of ballistic targets with rejection options. J Xi'an Jiaotong Univ 52(4):132\u2013138","journal-title":"J Xi'an Jiaotong Univ"},{"issue":"5","key":"1642_CR30","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10994-007-5013-y","volume":"68","author":"T Pietraszek","year":"2007","unstructured":"Pietraszek T (2007) On the use of ROC analysis for the optimization of abstaining classifiers. Mach Learn 68(5):137\u2013169","journal-title":"Mach Learn"},{"issue":"1","key":"1642_CR31","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1109\/TPAMI.2008.266","volume":"32","author":"S Escalera","year":"2010","unstructured":"Escalera S, Pujol O, Radeva P (2010) On the Decoding Process in Ternary Error-Correcting Output Codes. IEEE Trans Pattern Analysis and Machine Intelligence 32(1):120\u2013134","journal-title":"IEEE Trans Pattern Analysis and Machine Intelligence"},{"issue":"1","key":"1642_CR32","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1109\/TNN.2003.820841","volume":"15","author":"A Passerini","year":"2004","unstructured":"Passerini A, Pontil M, Frasconi P (2004) New Results on Error Correcting Output Codes of Kernel Machines. IEEE Trans Neural Netw 15(1):45\u201354","journal-title":"IEEE Trans Neural Netw"},{"issue":"5","key":"1642_CR33","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.knosys.2018.05.037","volume":"158","author":"JJ Bi","year":"2018","unstructured":"Bi JJ, Zhang CS (2018) An empirical comparison on state-of-the-art multi-class imbalance learning algorithms and a new diversified ensemble learning scheme. Knowl-Based Syst 158(5):81\u201393","journal-title":"Knowl-Based Syst"},{"issue":"7","key":"1642_CR34","first-page":"1","volume":"35","author":"J Demsar","year":"2006","unstructured":"Demsar J (2006) Statistical Comparisons of Classifiers over Multiple Data Sets. Machine Learning Research 35(7):1\u201330","journal-title":"Machine Learning Research"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-020-01642-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-020-01642-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-020-01642-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T13:46:52Z","timestamp":1620049612000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-020-01642-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,1]]},"references-count":34,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["1642"],"URL":"https:\/\/doi.org\/10.1007\/s10489-020-01642-2","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,1]]},"assertion":[{"value":"1 May 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}