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Simultaneously, we give some ideal and important properties of La\u03b5, such as boundedness, nonconvexity and robustness. Furthermore, a new binary classification learning method is proposed via introducing La\u03b5, which is called the robust twin support vector machine (Linex-TSVM). Linex-TSVM can not only reduce the influence of outliers on Linex-SVM, but also improve the classification performance and robustness of Linex-SVM. Moreover, the effect of outliers on the model can be greatly reduced by introducing two regularization terms to realize the structural risk minimization principle. Finally, a simple and efficient iterative algorithm is designed to solve the non-convex optimization problem Linex-TSVM, and the time complexity of the algorithm is analyzed, which proves that the model satisfies the Bayes rule. Experimental results on multiple datasets demonstrate that the proposed Linex-TSVM can compete with the existing methods in terms of robustness and feasibility.<\/jats:p>","DOI":"10.3390\/s22176583","type":"journal-article","created":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T03:55:38Z","timestamp":1662004538000},"page":"6583","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Capped Linex Metric Twin Support Vector Machine for Robust Classification"],"prefix":"10.3390","volume":"22","author":[{"given":"Yifan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}]},{"given":"Guolin","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,31]]},"reference":[{"key":"ref_1","unstructured":"Vapnik, V.N. 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