报 告 人：凌晨 教授
报告题目：Transformed low tubal-rank approximations of third order tensors via frequent directions
报告时间：2025年03月19日（周三）下午4：00
报告地点：静远楼1508会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
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。曾任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、中国运筹学会理事、中国系统工程学会理事、浙江省数学会常务理事等。现任国际期刊 Pacific Journal of Optimization编委、Statistics, Optimization & Information Computing编委。近十余年来，主持国家自科基金和浙江省自科基金各多项(其中含省基金重点项目1项)。在Math. Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等国内外重要刊物发表论文多篇。
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.
