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：我们对低级别非负矩阵近似问题提出了基于随机草图的新的近似交替投影方法:找到非负矩阵的低位近似值,该矩阵是非负矩阵,但其因素可能是任意的。我们计算了拟议方法的计算复杂性,并评估了其在数字实验中的性能。与已知的确定性交替投影方法的比较表明,随机投影方法更快,显示出相似的趋同性。