报告题目：Robust multi-class geometric twin support vector machine with a fast stochastic algorithm

报 告 人：齐凯博士（重庆国家应用数学中心）

报告时间：2025年10月26日（星期日）11:10-11:50

报告地点：数学大楼报告厅三（814）

参加人员：教师、研究生、本科生

报告摘要：Twin support vector machine (TSVM) is a well-known variant of support vector machine. However, in face of complex real-world problems, TSVM is confronted with significant challenges: 1) it can only deal with binary classification problems; 2) since adopting the hinge loss, TSVM is highly sensitive to noise and outliers; 3) and lots of existing algorithms solve the dual problem of TSVM and heavily relate to the sample size, which impedes its efficiency and application on large-scale datasets. To tackle these issues, inspired by the one-versus-one-versus-rest strategy, we propose a novel fuzzy geometric twin support vector machine for robust multi-class classification problems. First, by incorporating the concept of the average hyperplane, we construct the multi-class geometric twin support vector machine (MGTSVM). Unlike most existing multi-class TSVMs, MGTSVM maintains consistency between training and prediction processes while enabling superior performance. Second, we develop a robust weighting scheme to mitigate the impact of noise and outliers using relative density. Departing from Euclidean distance, this scheme employs Mahalanobis distance, offering greater flexibility and efficiency. Combining with MGTSVM, we propose the robust fuzzy MGTSVM (FMGTSVM). Third, instead of solving the dual problem, we implement a fast stochastic gradient descent algorithm for directly optimizing the primal problem. Convergence analysis shows the sample size-free training time cost. Compared with other famous multi-class SVMs reported in the literature, experiments on synthetic and benchmark datasets demonstrate the superiorities of the proposed FMGTSVM.

报告人简介：齐凯，统计学博士。西部科学城（重庆）金凤凰青年人才，重庆市优秀博士论文获得者。现为重庆国家应用数学中心讲师。研究兴趣包括高维复杂数据分类，半监督学习，支持向量机，稀疏降维学习等。已在IEEE Transactions on Neural Networks and Learning Systems（TNNLS）、Knowledge-Based Systems（KBS）、Expert Systems with Applications（ESWA）等国内外重要刊物上发表论文10余篇。现主持国家自然科学基金青年项目1项、重庆市自然科学基金面上项目1项和重庆市教委科技青年项目1项，参与多个横向和纵向项目。