T-product factorization based method for matrix and tensor completion problems

发布时间：2022-05-31 作者：浏览次数：

Speaker:	张新珍	DateTime:	2022年6月6日（周一）上午10：30-11：30
Brief Introduction to Speaker: 张新珍，天津大学副教授。		Place:	腾讯会议（会议号：993738339）
Abstract: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 an reweighted tensor factorization algorithm...