讲座人介绍： 

张雄军, 华中师范大学数学与统计学学院副教授，博士生导师. 2017年博士毕业于湖南大学, 2015年11月-2016年11月香港浸会大学博士交换生，2020年9月-2021年9月香港大学博士后，2019年获湖南省优秀博士学位论文. 主要研究方向包括张量优化和图像处理, 目前已在包括SIAM J. Imaging Sci., SIAM J. Sci. Comput., Appl. Comput. Harmon. Anal., IEEE TIT, IEEE TPAMI, IEEE TNNLS, Inverse Problems等期刊发表论文30余篇.

讲座简介：

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding matrices of a tensor, which may be suboptimal. In order to explore the low-rankness of the underlying tensor effectively, we propose a nonconvex model based on transformed tensor nuclear norm for low-rank tensor learning. Specifically, a family of nonconvex functions are employed onto the singular values of all frontal slices of a tensor in the transformed domain to characterize the low-rankness of the underlying tensor. An error bound between the stationary point of the nonconvex model and the underlying tensor is established under restricted strong convexity on the loss function (such as least squares loss and logistic regression) and suitable regularity conditions on the nonconvex penalty function. By reformulating the nonconvex function into the difference of two convex functions, a proximal majorization-minimization (PMM) algorithm is designed to solve the resulting model. Then the global convergence and convergence rate of PMM are established under very mild conditions. Numerical experiments are conducted on tensor completion and binary classification to demonstrate the effectiveness of the proposed method over other state-of-the-art methods.