秩一张量补全问题

2024.07.25

投稿:龚惠英部门:理学院浏览次数:

活动信息

报告题目 (Title):The Rank-1Tensor Completion Problem(秩一张量补全问题)

报告人 (Speaker):Jiawang Nie(University of California, San Diego)

报告时间 (Time):2024年07月29日(周一) 10:00

报告地点 (Place):校本部GJ403

邀请人(Inviter):周安娃

主办部门:理学院数学系

报告摘要: We discuss the rank-1 tensor completion problem for cubic order tensors. First of all, we show that this problem is equivalent to a special rank-1 matrix recovery problem. We propose both nuclear norm relaxation and moment relaxation methods for solving the resulting rank-1 matrix recovery problem. The nuclear norm relaxation sometimes get a rank- tensor completion, while sometimes it does not. When it fails, we apply the moment hierarchy of semidefinite programming relaxations to solve the rank- matrix recovery problem. The moment hierarchy can always get a rank- tensor completion, or detect its nonexistence. In particular, when the tensor is strongly rank-1 completable, we show that the problem is equivalent to a rank-1 matrix completion problem and it can be solved by an iterative formula. Therefore, much larger size problems can be solved efficiently for strongly rank-completable tensors. Numerical experiments are shown to demonstrate the efficiency of these proposed methods.

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