学术报告——张新珍副教授（天津大学）

报告名称：T-product factorization based method for matrix and tensor completion problems

主讲人：张新珍 副教授

邀请人：莫长鑫 讲师

时间：2022年6月21日   10:00

地点：腾讯会议（ID：774 417 922）

主办单位：数学科学学院

报告摘要

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency. For a matrix completion problem, we establish a relationship between matrix rank and tensor tubal rank, and reformulate matrix completion problem as a third order tensor completion problem. For the reformulated tensor completion problem, we adopt a two-stage strategy based on tensor factorization algorithm. In this way, a matrix completion problem of big size can be solved via some matrix computations of smaller sizes. For a third order tensor completion problem, to fully exploit the low rank structures, we introduce the double tubal rank which combines the tubal rank of two tensors, original tensor and the reshaped tensor of the mode-3 unfolding matrix of original tensor. Based on this, we propose a reweighted tensor factorization algorithm for third order tensor completion. Extensive numerical experiments demonstrate that the proposed methods outperform state-of-the-art methods in terms of both accuracy and running time.

专家简介

张新珍，天津大学数学学院英才副教授，于2010年获得香港理工大学博士学位，主要研究方向为张量计算、多项式优化与图像处理，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，目前共主持国家自然科学基金面上项目（两项）与青年基金（一项）。