题目：Newton method for nonconvex fusion regularized clustering

摘要：Clustering is one of the fundamental techniques of data analysis and is widely used in image processing, bioinformatics, social networking, etc. In this talk, we will introduce the fusion regularized clustering, which has received much attention for not requiring to specify the number of clusters beforehand. To overcome the biased estimation caused by convex regularization terms, we propose a nonconvex discontinuous fusion regularized clustering model based on the L0 penalty function, which is boiled down to a composite row sparsity regularized (cRSR) problem. Theoretically, we first establish the relationships among the critical stationary point, α-stationary point, strong α-stationary point, and the local/global optimal solution of cRSR problem. Then, a crucial stationary equation is derived from the (strong) α-stationary point. Computationally, we design an easy-to-implement Newton method for the stationary equation, and establish its quadratic convergence rate and iteration complexity under some mild assumptions. Finally, extensive experimental results in clustering and trend filtering are presented to show that the proposed method has good numerical performance.

报告时间：2023年10月30日 15:30-16:30

报告地点：Betway88211教室

报告人简介：孔令臣，教授，博士生导师，中国运筹学会数学规划分会理事长，北京交通大学数学与统计学院副经理。主要从事对称锥互补问题和最优化、稀疏优化、低秩矩阵优化、高维数据聚类、矩阵回归、统计优化与学习、医学成像等方面的研究。在《Mathematical Programming》、《SIAM Journal on Optimization》、《IEEE Transactions on Pattern Analysis and Machine Intelligence》、《IEEE Transactions on Signal Processing》、《Technometrics》、《Statistica Sinica》、《Electronic Journal of Statistics》等期刊发表论文60余篇。主持国家自然科学基金面上项目“高维稳健隐私回归的优化模型理论与算法研究”“高维聚类的结构矩阵优化理论与算法”、“高维约束矩阵回归的优化理论与算法”、“矩阵秩极小问题的松弛理论与算法研究”和专项项目“统计优化与人工智能天元数学交流项目”等, 参与重点项目“大规模稀疏优化问题的理论与算法”以及973课题等。曾获中国运筹学会青年奖，教育部自然科学二等奖和北京市高等公司产品成果一等奖等。