一种最优成对合并算法提升非负矩阵分解的质量与一致性
An optimal pairwise merge algorithm improves the quality and consistency of nonnegative matrix factorization
AI总结：
针对非负矩阵分解（NMF）易收敛到差局部极小值、解一致性差的问题，提出高维空间执行NMF加可解析成对合并分量的方法，能得到更优局部解、提升一致性且兼容多种NMF算法，计算性能与现有方法相当。
摘要：
非负矩阵分解（Non-negative matrix factorization, NMF）是特征提取的关键技术，广泛应用于源分离领域。然而，现有算法可能收敛到较差的局部极小值，或是收敛到多个目标值相近但特征参数化不同的极小值中的某一个。本文表明，通过在高维特征空间中执行NMF，再采用可解析求解的成对合并策略迭代合并分量，可缓解上述部分缺陷。实验结果显示，该方法能帮助非理想NMF解逃逸到更优的局部最优解，提升解的一致性。尽管增加了额外步骤，该方法通过减少鞍点附近“平台现象”的出现，计算性能与已有方法相当。此外，结果还表明该方法兼容不同的NMF算法，可推荐为大多数NMF应用的优选方案。
英文摘要：
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value but differing feature parametrizations. Here we show that some of these weaknesses may be mitigated by performing NMF in a higher-dimensional feature space and then iteratively combining components with an analytically-solvable pairwise merge strategy. Experimental results demonstrate our method helps non-ideal NMF solutions escape to better local optima and achieve greater consistency of the solutions. Despite these extra steps, our approach exhibits similar computational performance to established methods by reducing the occurrence of "plateau phenomenon" near saddle points. Moreover, the results also illustrate that our method is compatible with different NMF algorithms. Thus, this can be recommended as a preferred approach for most applications of NMF.
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