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 yields a sequence of standard low-rank matrix completion problems in our setting. 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. Our numerical studies and application to a real-data example illustrate that MMGN outputs comparable if not more accurate estimates, is often significantly faster, and is less sensitive to the spikiness of the underlying matrix than existing methods.

翻译：在1比特矩阵补全中，目标是从部分二进制观测中估计潜在的核数矩阵。我们提出了一种名为MMGN的1比特矩阵补全新方法。该方法基于极大化-最小化（MM）原理，在我们设定中能够生成一系列标准的核数矩阵补全子问题。我们采用因子化方法显式强制施加假定的核数结构来求解每个子问题，随后应用高斯-牛顿方法。数值实验及真实数据应用案例表明：MMGN在输出估计精度相当甚至更优的同时，往往具有显著更快的计算速度，且对潜在矩阵的尖峰性比现有方法更不敏感。