基于多源共享因子的多张量填充  

Multi-tensor completion with shared factors from multiple sources

作　　者：张骁[1] 胡清华[1] 廖士中[1] 

机构地区：[1]天津大学计算机科学与技术学院,天津300350

出　　处：《中国科学：信息科学》2016年第7期819-833,共15页Scientia Sinica(Informationis)

基　　金：国家自然科学基金重点项目(批准号:61432011);国家自然科学基金(批准号:61170019)资助项目

摘　　要：张量填充在数据挖掘、机器学习、生物信号处理等领域有着广泛的应用.现有的张量填充方法多在低秩假设的前提下对单独的张量进行填充,然而由于张量数据的复杂结构,张量填充的精度通常较低.为此,研究不同来源多个张量同时填充的方法.首先,利用Tucker分解将多源张量填充问题转换为最小二乘问题.然后,假设不同来源的张量在共享模式上具有共同的信息,为Tucker分解构造共享的因子矩阵集,提取多源张量在共享模式上的共同潜在结构,进而建立基于共享因子的多源张量填充(SF-MTC)方法.最后,利用非线性共轭梯度法和奇异值分解(SVD)快速求解Tucker分解的因子矩阵集及核心张量,完成同时对多个张量的填充,并进一步分析了SF-MTC的计算复杂度.在人工及实际数据集上的实验结果表明,所提出的SF-MTC能提高张量填充的求解效率,并在具有相关性的多源张量数据集上得到更高的填充精度.Tensor completion has been widely applied in data mining, machine learning, and biomedical signal processing. Most existing tensor completion methods recover a single tensor with low-rank assumption and exhibit low accuracy because of the complicated structures of tensor data. We address this issue by proposing a completion method based on a multiple sources tensors. Firstly, we formulate the least-squares problems for multiple sources tensor completion by using a Tucker decomposition. Then, we assume that tensors from different sources have common information at the shared modes, and create the shared factor matrices set of the Tucker decomposition from which the common latent structure from the shared modes can be extracted. Further, we develop a multiple sources tensor completion method with shared factors（SF-MTC）. Finally, we utilize a nonlinear conjugate gradient method and singular value decomposition to compute the factor matrices and core tensors of the Tucker decomposition, and recover the tensors from multiple sources simultaneously. We also analyze the computational complexity of the SF-MTC. Experimental results obtained with both synthetic and real data demonstrate that the SF-MTC is efficient for recovering multiple tensors, and accurate on multiple related tensor datasets.

关 键 词：张量填充 Tucker分解 共享因子 非线性共轭梯度法 奇异值分解 

分 类 号：O183.2[理学—数学]