報(bào) 告 人：凌晨 教授

報(bào)告題目：Transformed low tubal-rank approximations of third order tensors via frequent directions

報(bào)告時(shí)間：2025年03月19日（周三）下午4：00

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       凌晨，杭州電子科技大學(xué)理學(xué)院教授，博士生導(dǎo)師。曾任中國(guó)運(yùn)籌學(xué)會(huì)數(shù)學(xué)規(guī)劃分會(huì)副理事長(zhǎng)、中國(guó)經(jīng)濟(jì)數(shù)學(xué)與管理數(shù)學(xué)研究會(huì)副理事長(zhǎng)、中國(guó)運(yùn)籌學(xué)會(huì)理事、中國(guó)系統(tǒng)工程學(xué)會(huì)理事、浙江省數(shù)學(xué)會(huì)常務(wù)理事等。現(xiàn)任國(guó)際期刊 Pacific Journal of Optimization編委、Statistics, Optimization & Information Computing編委。近十余年來，主持國(guó)家自科基金和浙江省自科基金各多項(xiàng)(其中含省基金重點(diǎn)項(xiàng)目1項(xiàng))。在Math. Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等國(guó)內(nèi)外重要刊物發(fā)表論文多篇。 

報(bào)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.