More recently, an Approximate SVD Based on Qatar Riyal (QR) Decomposition (CSVD-QR) method for matrix complete problem is presented, whose computational complexity is $O(r^2(m+n))$, which is mainly due to that $r$ is far less than $\min\{m,n\}$, where $r$ represents the largest number of singular values of matrix $X$. What is particularly interesting is that after replacing the nuclear norm with the $L_{2,1}$ norm proposed based on this decomposition, as the upper bound of the nuclear norm, when the intermediate matrix $D$ in its decomposition is close to the diagonal matrix, it will converge to the nuclear norm, and is exactly equal, when the $D$ matrix is equal to the diagonal matrix, to the nuclear norm, which ingeniously avoids the calculation of the singular value of the matrix. To the best of our knowledge, there is no literature to generalize and apply it to solve tensor complete problems. Inspired by this, in this paper we propose a class of tensor minimization model based on $L_{2,1}$ norm and CSVD-QR method for the tensor complete problem, which is convex and therefore has a global minimum solution.
翻译:最近,根据卡塔尔里亚尔(QR)分解(CSVD-QR)的基质完整问题的方法,提出了一个基于卡塔尔里亚尔(QR)分解(CSVD-QR)法的基质完整问题,其计算复杂性为O(r_2(m+n)美元)美元,这主要是由于美元远远低于美元(m)美元(m),而美元是基质美元的最大值。特别有趣的是,在用基于这一分解(作为核规范的上限)提出的标准取代核规范之后,当中间基质(CSV-Q)在分解时,当中间基质的美元接近对角基质时,其计算复杂性将达到核规范,而当美元等于美元(mungn)美元(m),而美元代表基质(x美元)的最大值是最大值。据我们所知,没有文献可以概括和运用该标准解决高压(x)问题。因此,在本文件中,当中间基质(C-R_x)标准中,我们提出一个最起码的SAR(x)标准是C_Q)全球标准。