報 告 人：凌晨 教授

報告題目：Transformed low tubal-rank approximations of third order tensors via frequent directions

報告時間：2025年03月19日（周三）下午4：00

報告地點：靜遠樓1508會議室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

       凌晨，杭州電子科技大學理學院教授，博士生導師。曾任中國運籌學會數學規劃分會副理事長、中國經濟數學與管理數學研究會副理事長、中國運籌學會理事、中國系統工程學會理事、浙江省數學會常務理事等。現任國際期刊 Pacific Journal of Optimization編委、Statistics, Optimization & Information Computing編委。近十余年來，主持國家自科基金和浙江省自科基金各多項(其中含省基金重點項目1項)。在Math. Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等國內外重要刊物發表論文多篇。 

報告摘要： 

       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.