学术报告报告题目: Tensor Robust Principal Component Analysis Based on a Two-Layer Tucker Rank Minimization Model
报 告 人: 黄正海 教授
报告时间: 2025年6月28日（星期六）14:30-16:30
地 点：37号楼3A02
邀 请 人: 潘少华教授
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数学学院
2025年6月25日
报告摘要：
Tensor robust principal component analysis (TRPCA) has attracted extensive researches and been widely used in various areas. In this talk, we focus on TRPCA based on the Tucker rank. Considering that computing singular value decompositions (SVDs) of all unfolding matrices in the convex relaxation model of TRPCA based on the Tucker rank is highly time consuming, we propose a two-layer TRPCA model (TTRPCA) based on the convex relaxation model. In TTRPCA, we select a mode according to the nuclear norm of all unfolding matrices, and only need to compute SVD of the matrix unfolded along this mode, which can capture more information of the original data with low-rankness compared with other unfolding matrices. Moreover, we establish a generalized nonconvex two-layer TRPCA model (NTRPCA). Unlike existing methods which usually use a specific nonconvex function, NTRPCA uses a class of nonconvex functions to approximate the rank function and the L0 norm to more accurately capture the low rank structure and the sparsity. After that, we establish an error bound of the proposed NTRPCA model, which still holds for the TTRPCA model, and give some comparisons of cases using specific nonconvex functions. An alternating direction method of multipliers algorithm with convergence guarantee is then developed to solve the NTRPCA (as well as the TTRPCA) model. Finally, extensive numerical experiments on various datasets demonstrate the superior performance of proposed models in comparison with several state-of-the-art TRPCA methods.
报告人简介：
黄正海，天津大学数学学院教授、博士生导师。1999年博士毕业于复旦大学。主要从事最优化理论、算法及其应用方面的研究工作，在求解互补与变分不等式问题、对称锥优化与对称锥互补问题、稀疏优化、张量优化、核磁共振医学成像、人脸识别等方面取得了一系列有意义的成果。目前的主要研究兴趣是稀疏优化、张量优化、以及机器学习中的优化理论方法及其应用。已发表SCI检索论文140余篇，代表作发表于最优化领域顶刊Mathematical Programming和SIAM Journal on Optimization、数值代数顶刊SIAM Journal on Matrix Analysis and Applications、图像处理顶刊SIAM Journal on Imaging Sciences、信息科学顶刊IEEE Transactions on Information Theory、信息监控顶刊IEEE Transactions on Information Forensics and Security、信号处理顶刊IEEE Transactions on Signal Processing等。连续获得多项国家自然科学基金资助。曾获得中科院优秀博士后奖和教育部高等学校自然科学奖二等奖。目前为中国运筹学会数学规划分会副理事长；国际期刊《Pacific Journal of Optimization》、《Applied Mathematics and Computation》、《Asia-Pacific Journal of Operational Research》和《Optimization,Statistics & Information Computing》的编委、中国核心期刊《运筹学学报》的编委。