Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery

This repository contains MATLAB code to implement a basic variant of the Harmonic Mean Iteratively Reweighted Least Squares (HM-IRLS) algorithm for low-rank matrix recovery, in particular for the low-rank matrix completion problem, and to reproduce the experiments described in the paper:

C. Kümmerle, J. Sigl. "Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery", to appear in the Journal of Machine Learning Research (JMLR). Available online: https://arxiv.org/abs/1703.05038

The main file is HM_IRLS.m. See also the example scripts:

• script_mc_comparisons.m - Comparison script between HM-IRLS and two other algorithms on random matrix completion data
• script_small_example_IRLSvariants.m - Script illustrating the small example of Section 3 of the paper, comparing HM_IRLS with other IRLS variants for the problem
• script_HM_IRLS_Figure3.m - Script reproducing experiment of Figure 3 of the paper (convergence rates of HM-IRLS and other IRLS variants for easy problems)
• script_HM_IRLS_Figure4.m - Script reproducing experiment of Figure 4 of the paper (convergence rates of HM-IRLS and other IRLS variants for hard problems)
• script_HM_IRLS_Figure5.m - Script reproducing experiment of Figure 5 of the paper (convergence rates of HM-IRLS and other IRLS variants for very hard problems)

Version history

• Version 1.1, updated 10/01/2018
• Version 1.0, 3/14/2017

Author

Christian Kümmerle (website)

Acknowledgments

For the purpose of comparison with other popular algorithmic approaches, we included code by

• Bart Vandereycken ("LRGeomCG"), corresponding to the paper "Low-Rank Matrix Completion by Riemannian Optimization", SIAM J. Optim., 23(2), 1214–1236.
• Zaiwen Wen, Wotao Yin and Yin Zhang ("LMaFit"), corresponding to the paper "Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm", Math. Prog. Comp. (2012) 4: 333.