Non-negative matrix factorization (NMF) has become a popular method for learning interpretable patterns from data. As one of the variants of standard NMF, convolutive NMF (CNMF) incorporates an extra time dimension to each basis, known as convolutive bases, which is well suited for representing sequential patterns. Previously proposed algorithms for solving CNMF use multiplicative updates which can be derived by either heuristic or majorization-minimization (MM) methods. However, these algorithms suffer from problems, such as low convergence rates, difficulty to reach exact zeroes during iterations and prone to poor local optima. Inspired by the success of alternating direction method of multipliers (ADMMs) on solving NMF, we explore variable splitting (i.e., the core idea of ADMM) for CNMF in this article. New closed-form algorithms of CNMF are derived with the commonly used β -divergences as optimization objectives. Experimental results have demonstrated the efficacy of the proposed algorithms on their faster convergence, better optima, and sparser results than state-of-the-art baselines.

中文翻译：

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卷积非负矩阵分解乘法器的交替方向方法。

非负矩阵分解 (NMF) 已成为从数据中学习可解释模式的流行方法。作为标准 NMF 的变体之一，卷积 NMF (CNMF) 在每个基础上结合了额外的时间维度，称为卷积基础，非常适合表示顺序模式。先前提出的用于求解 CNMF 的算法使用乘法更新，可以通过启发式或多数最小化 (MM) 方法导出。然而，这些算法存在收敛速度低、迭代过程中难以达到精确零点以及容易出现局部最优等问题。受交替方向乘子法（ADMM）在求解 NMF 方面的成功启发，我们在本文中探索了 CNMF 的变量分裂（即 ADMM 的核心思想）。以常用的β散度为优化目标，推导了新的CNMF封闭式算法。实验结果证明了所提出的算法比最先进的基线具有更快的收敛速度、更好的最优值和更稀疏的结果的功效。