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To address these problems, we propose a novel method based on the capped \u21131 norm and a graph-based regularizer to deal with label noise. In the proposed algorithm, we utilize the capped \u21131 norm instead of the \u21131 norm. The used norm can inherit the advantage of the \u21131 norm, which is robust to label noise to some extent. Moreover, the capped \u21131 norm can adaptively find extremely mislabeled instances and eliminate the corresponding negative influence. Additionally, the proposed algorithm makes full use of the mislabeled instances under the graph-based framework. It can avoid wasting collected instance information. The solution of our algorithm can be achieved through an iterative optimization approach. We report the experimental results on several UCI datasets that include both binary and multi-class problems. The results verified the effectiveness of the proposed algorithm in comparison to existing state-of-the-art classification methods.<\/jats:p>","DOI":"10.3233\/jifs-200432","type":"journal-article","created":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T12:12:48Z","timestamp":1611922368000},"page":"4051-4063","source":"Crossref","is-referenced-by-count":0,"title":["Capped \u21131-norm regularized least squares classification with label noise"],"prefix":"10.1177","volume":"40","author":[{"given":"Zhi","family":"Yang","sequence":"first","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haitao","family":"Gan","sequence":"additional","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan, China"},{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Wuhan Institute of Technology, Hubei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Hubei University of Technology, Wuhan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-200432_ref1","doi-asserted-by":"crossref","first-page":"4311","DOI":"10.1109\/TSP.2006.881199","article-title":"K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation","volume":"54","author":"Aharon","year":"2006","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"2","key":"10.3233\/JIFS-200432_ref2","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/MIC.2013.20","article-title":"Quality control in crowdsourcing systems: Issues and directions","volume":"17","author":"Allahbakhsh","year":"2013","journal-title":"IEEE Internet Computing"},{"key":"10.3233\/JIFS-200432_ref3","first-page":"2399","article-title":"Manifold regularization: A geometric framework for learning from labeled and unlabeled examples","volume":"7","author":"Belkin","year":"2006","journal-title":"Journal of Machine Learning Research"},{"key":"10.3233\/JIFS-200432_ref4","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.neucom.2014.10.083","article-title":"Correction of noisy labels via mutual consistency check","volume":"160","author":"Bhadra","year":"2015","journal-title":"Neurocomputing"},{"issue":"6","key":"10.3233\/JIFS-200432_ref5","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1016\/j.neucom.2010.10.015","article-title":"Lift: A new framework of learning from testing data for face recognition","volume":"74","author":"Cao","year":"2011","journal-title":"Neurocomputing"},{"key":"10.3233\/JIFS-200432_ref6","unstructured":"Brodley C.E. , M.A.F., Identifying and eliminating mislabeled training instances. 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