Guo Youdong, Holy Timothy E
Department of Neuroscience, Washington University in St. Louis, St. Louis, MO, 63130, USA.
Department of Neuroscience and Biomedical Engineering, Washington University in St. Louis, St. Louis, MO, 63130, USA.
IEEE Trans Signal Process. 2025;73:2862-2878. doi: 10.1109/tsp.2025.3585893. Epub 2025 Jul 4.
Non-negative matrix factorization (NMF) is widely used for dimensionality reduction of large datasets and is an important feature extraction technique for source separation. However, NMF 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 efficient and analytically solvable pairwise merge strategy. Both theoretical and experimental results demonstrate that our method allows optimizers to escape poor minima and achieve greater consistency of the solutions. Despite these extra steps, our approach exhibits computational performance similar to established methods by reducing the occurrence of "plateau phenomena" near saddle points. Our method is compatible with a variety of standard NMF algorithms and exhibits an average performance that exceeds all algorithms tested. Thus, this can be recommended as a preferred approach for most applications of NMF.
非负矩阵分解（NMF）被广泛用于大型数据集的降维和源分离的重要特征提取技术。然而，NMF算法可能会收敛到较差的局部最小值，或者收敛到具有相似目标值但特征参数化不同的几个最小值之一。在这里，我们表明，通过在更高维特征空间中执行NMF，然后使用高效且可解析求解的成对合并策略迭代组合组件，可以减轻其中一些弱点。理论和实验结果均表明，我们的方法使优化器能够逃离较差的最小值并实现更高的解的一致性。尽管有这些额外的步骤，但我们的方法通过减少鞍点附近“平台现象”的发生，展现出与现有方法相似的计算性能。我们的方法与各种标准NMF算法兼容，并且平均性能超过所有测试算法。因此，对于NMF的大多数应用，这可以作为首选方法推荐。
