报告题目：Transformed low tubal-rank approximations of third order tensors via frequent directions
报 告 人：凌晨 (杭州电子科技大学 教授)
报告时间：2023年11月10日 8:45开始
报告地点：9-218
报告摘要：Tensor low rank approximation is an important tool in tensor data analysis and processing. In the sense of T-product derived from general invertible transformation, the best low tubal rank approximation of third order tensors can be obtained through truncated T-SVD. In this talk, we first present two deterministic frequent directions type algorithms for near optimal low tubal rank approximations of third order tensors. Moreover, by combining the fast frequent directions type algorithm with the so-called random count sketch sparse embedding method, we propose a randomized frequent directions algorithm for near optimal low tubal rank approximations of third order tensors. Corresponding relative error bounds for the presented algorithms are derived. The related numerical examples on third order tensors of color image, grayscale video and synthetic data with larger scale illustrate the favorable performance of the presented methods compared to some existing methods.
报告人简介：凌晨，杭州电子科技大学理学院教授、博士生导师。主要研究方向为：非线性规划、变分不等式与互补问题、张量计算、多变量多项式优化、半无限规划、随机规划、多目标优化理论与应用等。现任中国运筹学会理事、中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长、浙江省数学会常务理事，国际ESI期刊 Pacific Journal of Optimization编委、国际期刊Statistics, Optimization & Information Computing编委，国家自然科学基金委数理科学部评审专家。近十年主持国家自科基金和浙江省自科基金各4项、其中省基金重点项目1项。在国内外重要刊物发表论文70余篇，其中SCI期刊论文50余篇，多篇发表在Math. Program.、SIAM J. Optim.和 SIAM J. Matrix Anal. and Appl. 、COAP、JOTA、JOGO等。
