The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems. However, it suffers from difficulties in effective solution of multi-classification and fast model selection. This work devotes to the fast regularization parameter tuning algorithm for the twin multi-class support vector machine. Specifically, a novel sample data set partition strategy is first adopted, which is the basis for the model construction. Then, combining the linear equations and block matrix theory, the Lagrangian multipliers are proved to be piecewise linear w.r.t. the regularization parameters, so that the regularization parameters are continuously updated by only solving the break points. Next, Lagrangian multipliers are proved to be 1 as the regularization parameter approaches infinity, thus, a simple yet effective initialization algorithm is devised. Finally, eight kinds of events are defined to seek for the starting event for the next iteration. Extensive experimental results on nine UCI data sets show that the proposed method can achieve comparable classification performance without solving any quadratic programming problem.
LIBTwinSVM: A Library for Twin Support Vector Machines
Iranian Research Institute for Information Science and Technology (IranDoc)（伊朗信息科学与技术研究院（IranDoc））；Islamic Azad University, North Tehran Branch（伊斯兰阿扎德大学北德黑兰分校）
Incremental and Decremental Fuzzy Bounded Twin Support Vector Machine
École de Technologie Supérieure - Université du Québec（魁北克大学高等技术学院）；University of Santa Catarina（圣卡塔琳娜大学）；SENAI Innovation Institute of Embedded Systems（巴西服务于工业的国家服务机构嵌入式系统创新研究所）
Granular-Balls based Fuzzy Twin Support Vector Machine for Classification
School of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；School of Information Science and Technology, Nantong University（南通大学信息科学与技术学院）；Department of Computer Science and Technology, Tongji University（同济大学计算机科学与技术系）
Use Digital Twins to Support Fault Diagnosis From System-level Condition-monitoring Data
CentraleSupélec（中央高等电力学院）；Université Paris-Saclay（巴黎-萨克雷大学）；Shenzhen Weimin Institute for Reliability Systems Engineering（深圳伟民可靠性系统工程研究院）；Laboratoie Genie Industriel（工业工艺实验室）
A Robust Twin Parametric Margin Support Vector Machine for Multiclass Classification
School of Science and Technology, University of Camerino（科学与技术学院，坎皮诺大学）；Department of Management, Information and Production Engineering, University of Bergamo（管理、信息与生产工程系，贝拉姆多大学）
Kernel-Free Universum Quadratic Surface Twin Support Vector Machines for Imbalanced Data
Jan Evangelista Purkyně University（詹·埃瓦尔德·普日科夫大学）；Charles University（查尔斯大学）；American University（美国阿美利克大学）；University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；Northeastern University（东北大学）
Multi-Task Learning Based on Support Vector Machines and Twin Support Vector Machines: A Comprehensive Survey
Department of Computer Science, Faculty of Mathematical Sciences, Alzahra University（计算机科学系，数学科学学院，阿扎赫拉大学）；Department of Informatics, Faculty of Science, Jan Evangelista Purkyne University（信息系，科学学院，扬·埃万杰利斯塔·普日科夫斯基大学）；Department of Computer Engineering, Science and Research Branch, IAU（计算机工程系，科学与研究分支，伊阿大学）；Department of Industrial and Systems Engineering, University of Florida（工业与系统工程系，佛罗里达大学）
Transformer self-attention encoder-decoder with multimodal deep learning for response time series forecasting and digital twin support in wind structural health monitoring
Department of Mechanical Engineering, University of Bath（巴斯大学机械工程系）；Department of Civil Engineering, Zhejiang University（浙江大学土木工程系）
