Leveraging Joint-Diagonalization in Transform-Learning NMF

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at data representations suited to NMF. In this work, we relate TL-NMF the classical joint-diagonalization (JD) problem. We show that, when number of realizations sufficiently large, can be replaced by two-step approach -- termed as JD+NMF estimates through JD, prior NMF computation. contrast, found limited, not only no longer equivalent TL-NMF, but inherent low-rank constraint turns out an essential ingredient learn meaningful transforms for