报告题目：Guaranteed Sampling Flexibility for Low-tubal-rank Tensor Completion

报告人：Longxiu Huang (黄龙秀教授)

报告人单位：密歇根州立大学(Michigan State University)

报告时间：北京时间2024年11月22日上午9:00-10:00

         密歇根时间2024年11月21日晚上8:00-9:00

会议地点：#腾讯会议：437-247-046

主办单位：曲阜师范大学数学科学学院

报告摘要：

Tensor completion is an important topic in high-dimensional data analysis, with Bernoulli sampling and t-CUR sampling being two commonly used approaches. While Bernoulli sampling is widely studied, t-CUR sampling targets low-tubal-rank tensors through subtensors, yet both methods lack the adaptability required for many practical scenarios. In this talk, I introduce Tensor Cross-Concentrated Sampling (t-CCS), a novel sampling framework that extends the concept of cross-concentrated sampling from matrices to tensors. By bridging the gap between Bernoulli and t-CUR sampling, t-CCS offers enhanced flexibility and computational efficiency. I will present a sufficient condition for the successful recovery of low-rank tensors using t-CCS samples. Additionally, I will share a theoretical framework validating t-CUR via uniform random sampling and provide a detailed sampling complexity analysis for tensor completion under Bernoulli sampling. To complement the t-CCS framework, I will introduce the Iterative t-CUR Tensor Completion (ITCURTC) algorithm, an efficient non-convex approach designed for t-CCS-based tensor completion. Through extensive experiments on both synthetic and real-world datasets, I will demonstrate the practical effectiveness of the t-CCS model and the ITCURTC algorithm.

报告人简介：

Longxiu Huang (黄龙秀) is currently in the Department of Computational Mathematics, Science and Engineering and Department of Mathematics at Michigan State University. Dr. Huang received her PhD in Mathematics from Vanderbilt University with Prof. Akram Aldroubi and worked in UCLA before joining MSU in 2022. Her main research interests lie in Applied Harmonic Analysis, Numerical linear algebra, Data Analysis, Random matrix analysis, etc. She has 31 publications, including the top journal SIAM Journal on Matrix Analysis and Applications,SIAM Journal on Scientific Computing, SIAM Journal on Imaging Sciences, Applied and Computational Harmonic Analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, The Journal of Geometric Analysis and SIAM Journal of Discrete Mathematics, etc.