Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to represent the data containing the internal structure of multiple factors came into being. However, different from the matrix case, constructing reasonable sparse measure of tensor is a relatively difficult and very important task. Therefore, in this paper, we propose a new tensor sparsity measure called Tensor Full Feature Measure (FFM). It can simultaneously describe the feature information of each dimension of the tensor and the related features between two dimensions, and connect the Tucker rank with the tensor tube rank. This measurement method can describe the sparse features of the tensor more comprehensively. On this basis, we establish its non-convex relaxation, and apply FFM to low rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). LRTC and TRPCA models based on FFM are proposed, and two efficient Alternating Direction Multiplier Method (ADMM) algorithms are developed to solve the proposed model. A variety of real numerical experiments substantiate the superiority of the proposed methods beyond state-of-the-arts.
翻译:在整个科学和工程领域,作为有希望的模型,微粒稀少的模型是一个大有希望的方法,在科学和工程方面是一个巨大的成功。众所周知,各种实际应用的数据往往是由多种因素产生的,因此,使用高压来代表包含多种因素内部结构的数据。然而,与矩阵情况不同,建造合理稀少的高温测量是一个相对困难和非常重要的任务。因此,我们在本文件中提议了一个新的高温聚度测量法,称为Tensor全功能测量法(FFM)。它可以同时描述高压每个层面的特征信息以及两个层面之间的相关特征,并将塔克级与高压管级连接起来。这一测量法可以更全面地描述高压体位的稀少特征。在此基础上,我们确立其非凝固度放松度,将实况调查团应用于低级的高压完成(LRTC)和高压主要部件分析(TRPA)。基于实况调查团的LRTC和TRPCA模型被提出。两种高效的变向方向多动法(ADMM)算法(ADMM)可超越拟议的模型。各种实际的实数级检验方法。