We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.

翻译：我们提出了新的近似交替投影方法，基于随机草图技术，用于解决低秩非负矩阵近似问题：寻找一个非负矩阵的低秩近似，该近似保持非负性，但其中的因子可以为任意值。我们计算了所提方法的计算复杂度，并通过数值实验评估了其性能。与已知的确定性交替投影方法相比，随机方法速度更快，且展现出相似的收敛性质。