On the Identifiability of Transform Learning for Non-negative Matrix Factorization
Résumé
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.
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