  In 1-bit matrix completion, the aim is to estimate an underlying low-rank
matrix from a partial set of binary observations. We propose a novel method for
1-bit matrix completion called MMGN. Our method is based on the
majorization-minimization (MM) principle, which converts the original
optimization problem into a sequence of standard low-rank matrix completion
problems. We solve each of these sub-problems by a factorization approach that
explicitly enforces the assumed low-rank structure and then apply a
Gauss-Newton method. Using simulations and a real data example, we illustrate
that in comparison to existing 1-bit matrix completion methods, MMGN outputs
comparable if not more accurate estimates. In addition, it is often
significantly faster, and less sensitive to the spikiness of the underlying
matrix. In comparison with three standard generic optimization approaches that
directly minimize the original objective, MMGN also exhibits a clear
computational advantage, especially when the fraction of observed entries is
small.
