三阶张量的多管秩及相关低秩张量补全问题
Multi-Tubal Rank of Third Order Tensor and Related Low Rank Tensor Completion Problem
AI总结：
针对现有低管秩张量补全方法仅利用单模式低秩结构的不足，提出多管秩概念及对应低秩补全模型，结合时空特征改进模型，实验表明该方法在图像、视频等数据补全上优于现有方法。
摘要：
近年来，针对三阶张量的低管秩张量补全问题，一种基于张量分解的方法被提出，其性能优于部分现有方法。管秩仅定义在三阶张量的一个模式上，另外两个模式不具备低秩结构，也就是说，另外两个模式上的低秩结构是缺失的。受此启发，我们首先引入多管秩，随后建立了多管秩与Tucker秩之间的关系。基于多管秩，我们提出了一种新型低秩张量补全模型。针对该模型，我们采用了基于张量分解的方法，并建立了相应的收敛性分析。此外，时空特征是视频和网络流量张量数据的固有特征。为获得更优性能，我们充分利用这类特征，对所建立的张量补全模型进行改进，随后将基于张量分解的方法应用于改进后的模型。最后，我们在图像、视频和网络流量数据的补全任务上报告了数值结果，以验证所提方法的有效性。从报告的数值结果可以断定，我们的方法性能优于现有方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
