一个基于d阶张量奇异值分解的互联网流量数据恢复方法  

An Internet Traffic Data Completion Strategy with dth-Order Tensor Singular Value Decomposition

作　　者：段宇轩 刘金杰[1] DUAN Yuxuan;LIU Jinjie(National Center for Applied Mathematics in Chongqing,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学重庆国家应用数学中心,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2024年第4期84-93,共10页Journal of Chongqing Normal University:Natural Science

基　　金：重庆英才计划“包干制项目”(No.cstc2022ycjh-bgzxm0040);重庆市教育委员会科学技术研究项目(No.KJZD-K202200506);重庆师范大学校级基金项目(No.22XLB005);重庆国家应用数学中心科研项目(No.ncamc2022-msxm02)。

摘　　要：精准恢复互联网流量数据能降低不完全数据对网络任务过程的损害,因此,针对互联网流量数据的相似性和周期性这一时空特性,基于d阶张量奇异值分解(d阶T-SVD),结合时空正则化策略,对具有四阶张量结构性质的互联网流量数据构建了恢复模型。这一模型的核心在于能够深入挖掘数据的同时保留了内部复杂的结构特性,从而实现更高质量的数据恢复。采用交替极小化方法,设计了一种高效且稳定的算法,以实现对模型的精确求解。最后选取了2个真实的互联网流量数据集,模拟随机性缺失和结构性缺失的数据场景,对提出的方法进行了全面验证。实验结果表明,该方法在数据恢复性能上相较于现有方法,展现出明显的优势。The aim is to accurately recover Internet traffic data,which could reduce the negative impact caused by incomplete data on the network tasks.Since the traffic data could be represented by a fourth order tensor,and considering its spatiotemporal characteristics,an optimal recovery model was proposed based on dth-order tensor singular value decomposition(dth-order T-SVD)combined with spatiotemporal regularization strategies.The key feature of this model lies in its ability to deeply explore the data while preserving its internal complex structural properties,thereby achieving higher-quality data recovery.An efficient and stable algorithm is developed to solve this model accurately by utilizing the alternating minimization method.Finally,the proposed method was comprehensively validated by simulating both random and structural data loss scenarios on two real internet traffic datasets.Experimental results demonstrate that this method exhibits significant advantages in data recovery performance compared to existing methods.

关 键 词：互联网流量数据恢复 d阶张量奇异值分解 时空正则化 交替极小化 张量填充 

分 类 号：O221.2[理学—运筹学与控制论]