In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an NMF with additional sequential structure. This model is useful in a number of applications, such as audio source separation and neural sequence identification. While a number of heuristic algorithms have been proposed to solve CNMF, to the best of our knowledge no provably correct algorithms have been developed. We present an algorithm that takes advantage of the NMF model underlying CNMF and exploits existing algorithms for separable NMF to provably find a solution under certain conditions. Our approach guarantees the solution in low noise settings, and runs in polynomial time. We illustrate its effectiveness on synthetic datasets, and on a singing bird audio sequence.
翻译:在本文中,我们提出了一种在分离假设下对非负矩阵乘数进行混合的正确算法; CNMF是非负矩阵乘数(NMF)的混合变体,它作为非负矩阵乘数(NMF),具有额外的相继结构; 这个模型在音频源分离和神经序列识别等一些应用中有用; 虽然已经建议了一些超速算法,以解决CNMF, 以我们所知的最佳方式, 但没有开发出任何可调校正的算法; 我们提出了一种利用CNMF模型的算法, 并利用现有的算法, 使可分离的NMF在某些条件下找到解决办法; 我们的方法保证了低噪音环境中的解决方案, 并且运行在多种时间。 我们展示了它在合成数据集和歌唱鸟音序列上的有效性。