A generalized tri-factorization method for accurate matrix completion

Abstract

To improve the speeds of the traditional nuclear norm minimization methods, a fast tri-factorization method (FTF) was recently proposed for matrix completion, and it received widespread attention in the fields of machine learning, image processing and signal processing. However, its low convergence accuracy became increasingly obvious, limiting its further application. To enhance the accuracy of FTF, a generalized tri-factorization method (GTF) is proposed in this paper. In GTF, the nuclear norm minimization model of FTF is improved to a novel \({{\varvec{L}}}_{1,{\varvec{p}}}\)(0 < p < 2) norm minimization model that can be optimized very efficiently by using QR decomposition. Since the \({{\varvec{L}}}_{1,{\varvec{p}}}\) norm is a tighter relaxation of the rank function than the nuclear norm, the GTF method is much more accurate than the traditional methods. The experimental results demonstrate that GTF is more accurate and faster than the state-of-the-art methods.