We present an efficient low-rank approximation algorithm for non-negative tensors. The algorithm is derived from our two findings: First, we show that rank-1 approximation for tensors can be viewed as a mean-field approximation by treating each tensor as a probability distribution. Second, we theoretically provide a sufficient condition for distribution parameters to reduce Tucker ranks of tensors; interestingly, this sufficient condition can be achieved by iterative application of the mean-field approximation. Since the mean-field approximation is always given as a closed formula, our findings lead to a fast low-rank approximation algorithm without using a gradient method. We empirically demonstrate that our algorithm is faster than the existing non-negative Tucker rank reduction methods and achieves competitive or better approximation of given tensors.

翻译：我们为非负向性抗拉提供了一种高效的低级别近似算法。这种算法来自我们的两个发现:首先,我们通过将每个抗拉作为概率分布处理,表明对抗拉的一级近近近可被视为一种中位近近近近。第二,我们理论上为分配参数提供了足够条件,以减少塔克的抗拉等级;有趣的是,通过反复应用中位近近近可以实现这一充分条件。由于中位近近近总是作为一种封闭的公式,我们的调查结果导致一种不使用梯度方法的快速低级别近近近近近算法。我们从经验上证明,我们的算法比现有的非负级塔克降级方法更快,并且实现了对给定的抗拉的竞争性或更好近近近。