We revisit the problem of recovering a low-rank positive semidefinite matrix from rank-one projections using tools from optimal transport. More specifically, we show that a variational formulation of this problem is equivalent to computing a Wasserstein barycenter. In turn, this new perspective enables the development of new geometric first-order methods with strong convergence guarantees in Bures-Wasserstein distance. Experiments on simulated data demonstrate the advantages of our new methodology over existing methods.

翻译：我们再次探讨了利用最佳运输工具从一级预测中恢复低位正半无限制矩阵的问题。更具体地说,我们表明,这一问题的变式配方相当于计算瓦塞斯坦热点。 反过来,这一新的观点又有助于开发新的几何第一阶方法,在布雷斯-瓦瑟斯坦距离上提供强有力的趋同保证。 模拟数据的实验显示了我们新方法比现有方法的优势。