|| On the Identifiability of Transform Learning for Non-Negative Matrix Factorization
||Sixin Zhang, Emmanuel Soubies, Cédric Févotte, IRIT, France|
|Session||MLSP-19: Non-Negative Matrix Factorization|
|Session Time:||Wednesday, 09 June, 14:00 - 14:45|
|Presentation Time:||Wednesday, 09 June, 14:00 - 14:45|
|| Machine Learning for Signal Processing: [MLR-MFC] Matrix factorizations/completion|
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|| 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 themodel. This result is illustrated on a toy source separation problem which demonstrates the ability of TL-NMF to learn a suitable orthogonal basis.