报告人： 张新珍 副教授  天津大学

报告题目：Multi-Tubal Rank of Third Order Tensor and Related Low Rank Tensor Completion Problem

报告时间：2020/12/11 (周五)下午3：00-4：00      

地点：腾讯会议 ID： 822 896 342

报告校内联系人：郭 峰 副教授       联系电话：84708351-8088

报告摘要：

Recently, a tensor factorization based method for a low  tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods. Tubal rank is only defined on one mode of third order tensor without low rank structure in the other two modes. That is, low rank structures on the other two modes are missing. Motivated by this, we first introduce multi-tubal rank, and then establish a relationship between multi-tubal rank and Tucker rank. Based on the multi-tubal rank, we propose a novel low rank tensor completion model. For this model, a tensor factorization based method is applied. In addition, spatio-temporal characteristics are intrinsic features in video and internet traffic tensor data. To get better performance, we make full use of such features and improve the established tensor completion model. Then we apply tensor factorization based method for the improved model. Finally, numerical examples are reported on the completion of image, video and internet traffic data to show the efficiency of our proposed methods. From the reported numerical results, we can assert that our methods outperform the existing methods.

报告人简介：张新珍，2010年博士毕业于香港理工大学，现为天津大学数学学院副教授。目前主要从事张量计算与多项式优化方面的工作，研究论文发表于SIAM Journal on Optimization, SIAM Journal on Matrix Analysis and Applications 等优化领域的核心期刊。

数学科学学院

2020/12/9