嵌入空间的低秩张量填充算法  

Low Rank Tensor Completion Algorithm in Embedded Space

作　　者：杨庆圆 王川龙 YANG Qingyuan;WANG Chuanlong(School of Mathematics and Statistics,Laboratory of Engineering and Scientific Computing,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院工程科学计算实验室/数学与统计学院,山西晋中030619

出　　处：《太原师范学院学报（自然科学版）》2022年第4期28-34,共7页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：国家自然科学基金(11371275);太原师范学院研究生教育创新项目(SYYJSYC-2288)。

摘　　要：以高精度低秩张量填充算法为基础,提出了在嵌入空间中的低秩张量填充算法.先将缺失数据经过多向延迟嵌入变为高阶Hankel张量,再基于核范数最小化进行填充,最后使用多向延迟嵌入的逆操作得到最终的填充数据.通过数值实验表明,针对张量的条状或块状缺失,新算法比HaLRTC、DR-TR算法更有效.Based on the high accuracy low rank tensor completion algorithm,a low rank tensor completion algorithm in embedded space is proposed.Firstly,the missing data is transformed into a higher-order Hankel tensor by multi-way delay embedding.Then,a method is used for completing based on the nulear norm minimization.Finally,the inverse transform is used to obtain the completed data.And experimental results show that the new algorithm is more effective than HaLRTC and DR-TR algorithm for row and column fiber missing of tensor.

关 键 词：张量填充 多向延迟嵌入变换 高精度低秩张量填充算法 

分 类 号：O183.2[理学—数学]