Rethinking Non-Negative Matrix Factorization with Implicit Neural
  Representations
Krishna Subramani Paris Smaragdis Takuya Higuchi Mehrez Souden
Non-negative Matrix Factorization (NMF) is a powerful technique for analyzing
regularly-sampled data, i.e., data that can be stored in a matrix. For audio,
this has led to numerous applications using time-frequency (TF) representations
like the Short-Time Fourier Transform. However extending these applications to
irregularly-spaced TF representations, like the Constant-Q transform, wavelets,
or sinusoidal analysis models, has not been possible since these
representations cannot be directly stored in matrix form. In this paper, we
formulate NMF in terms of continuous functions (instead of fixed vectors) and
show that NMF can be extended to a wider variety of signal classes that need
not be regularly sampled.