论文标题
三阶张量和相关低等级张量完成问题的多管等级
Multi-Tubal Rank of Third Order Tensor and Related Low Rank Tensor Completion Problem
论文作者
论文摘要
最近，提出了一种基于张量的分解方法，用于低管升张量张量的完成问题，该问题的执行量比某些现有方法更好。在其他两种模式中，管等级仅在三阶张量的一种模式下定义。也就是说，缺少其他两种模式的低级结构。在此激励的基础上，我们首先引入多管等级，然后在多管等级和塔克等级之间建立关系。基于多管等级，我们提出了一种新型的低级张量完成模型。对于此模型，应用了基于张量分解的方法，并建立了相应的收敛性厌食。此外，时空特征是视频和互联网流量张量数据中的内在特征。为了获得更好的性能，我们充分利用此类功能并改善既定的张量完成模型。然后，我们将基于张量分解的方法应用于改进的模型。最后，报道了图像，视频和互联网流量数据的完成，以显示我们提出的方法的效率。从报告的数值结果中，我们可以断言我们的方法优于现有方法。
Recently, a tensor factorization based method for a low tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods. Tubal rank is only defined on one mode of third order tensor without low rank structure in the other two modes. That is, low rank structures on the other two modes are missing. Motivated by this, we first introduce multi-tubal rank, and then establish a relationship between multi-tubal rank and Tucker rank. Based on the multi-tubal rank, we propose a novel low rank tensor completion model. For this model, a tensor factorization based method is applied and the corresponding convergence anlysis is established. In addition, spatio-temporal characteristics are intrinsic features in video and internet traffic tensor data. To get better performance, we make full use of such features and improve the established tensor completion model. Then we apply tensor factorization based method for the improved model. Finally, numerical results are reported on the completion of image, video and internet traffic data to show the efficiency of our proposed methods. From the reported numerical results, we can assert that our methods outperform the existing methods.
