Non-negative matrix factorization with transform learning (TL-NMF) aims at estimating a short-time orthogonal transform that projects temporal data into a domain that is more amenable to NMF than off-the-shelf time-frequency transforms. In this work, we study the identifiability of TL-NMF under the Gaussian composite model. We prove that one can uniquely identify row-spaces of the orthogonal transform by optimizing the likelihood function of the model. This result is illustrated on a toy source separation problem which demonstrates the ability of TL-NMF to learn a suitable orthogonal basis.

中文翻译：

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关于非负矩阵分解的变换学习的可识别性

具有变换学习的非负矩阵分解 (TL-NMF) 旨在估计短时正交变换，该变换将时间数据投影到比现成的时频变换更适合 NMF 的域中。在这项工作中，我们研究了高斯复合模型下 TL-NMF 的可识别性。我们证明了通过优化模型的似然函数可以唯一地识别正交变换的行空间。这个结果在一个玩具源分离问题上得到了说明，该问题证明了 TL-NMF 学习合适的正交基的能力。