Non-negative matrix factorization for irregularly-spaced transforms

Non-negative factorizations of spectra have been a very popular tool for various audio tasks recently. A long-standing problem with these methods methods is that they cannot be easily applied on other kinds of spectral decompositions such as sinusoidal models, constant-Q transforms, wavelets and reassigned spectra. This is because with these transforms the frequency and/or time values are real-valued and not sampled on a regular grid. We therefore cannot represent them as a matrix that we can later factorize. In this paper we present a formulation of non-negative matrix factorization that can be applied on data with real-valued indices, thereby making the application of this family of methods feasible on a broader family of time/frequency transforms.