Fast and Accurate Low-Rank Tensor Completion Methods Based on QR Decomposition and L_2,1 Norm Minimization

by   HongBing Zhang, et al.
NetEase, Inc

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.


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