基于张量环分解的非精确的低秩填充算法  

A Inexact Low Rank Tensor Completion Algorithm Based on Tensor Ring Decomposition

作　　者：孟翔宇 温瑞萍 MENG Xiangyu;WEN Ruiping(Key Laboratory for Engineering&Computing Science,Shanxi Provincial Department of Education,Jinzhong 030619,China;Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]工程科学计算山西省高等学校重点实验室,山西晋中030619 [2]太原师范学院数学系,山西晋中030619

出　　处：《太原师范学院学报（自然科学版）》2022年第1期1-5,共5页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：国家自然科学基金(11371275);山西省自然科学基金(201901D211423)。

摘　　要：文章提出一种基于张量环分解的低秩填充算法.利用张量核因子决定存储信息的2-模展开来代替控制结构的1-模和3-模展开.虽然每次迭代不是最优下降,但保证了整体下降.从而减少了计算花费,提高了张量填充效率.最后通过实验验证了新算法的可行性.在精度一致的情况下,文章算法较之前算法快了近3倍.Based on tensor ring(TR)decomposition,a inexact low rank tensor completion algorithm is proposed.By employing the mode-2 unfolding matrix of core tensors to represents mode-1 unfolding matrix and mode-3’s,it ensures the global descending rather than optimal descent every iteration.The computational cost is reduced and efficiency is improved by employing proposed method.Finally,the experiments on real-world datasets were conducted to evaluate the performance of algorithm.The simulation experiment shows that the proposed algorithm is about 3 times faster than traditional algorithm without almost loss of accuracy.

关 键 词：张量填充 环分解 低秩 

分 类 号：O151.21[理学—数学]