Harmonic Mean Iteratively Reweighted Least Squares for low-rank matrix recovery

Abstract

We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of recovering a matrix X ∈ ℝd1 × d2 of rank r ≪ min(d 1 , d 2 ) from incomplete linear observations, solving a sequence of quadratic problems. The easily implementable algorithm, which we call Harmonic Mean Iteratively Reweighted Least Squares (HM-IRLS), is superior compared to state-of-the-art algorithms for the low-rank recovery problem in several performance aspects. More specifically, the strategy HM-IRLS uses to optimize a non-convex Schatten-p penalization to promote low-rankness carries three major strengths, in particular for the matrix completion setting.