A Fast Matrix Completion Method Based on Matrix Bifactorization and QR Decomposition

Abstract

The problem of recovering the missing values in an incomplete matrix, i.e., matrix completion, has attracted a great deal of interests in the fields of machine learning and signal processing. A matrix bifactorization method, which is abbreviated as MBF, is a fast method of matrix completion that has a better speed than the traditional nuclear norm minimization methods. However, it may become inaccurate and slow when solving matrices of not low rank. In this paper, an improved fast and accurate MBF method based on Qatar Riyal (QR) decomposition is proposed, which can be called FMBF-QR. On one side, the optimization problem of MBF is improved to be an iteratively reweighted $L_{2,1}$ norm minimization problem to enhance the accuracy of MBF. On the other side, the minimization problem of FMBF-QR is optimized very efficiently by using QR decomposition for improving the speed of MBF. Sufficient experimental results verify that FMBF-QR can converge with a higher accuracy and a faster speed than the traditional matrix completion methods.