Rethinking Non-Negative Matrix Factorization with Implicit Neural Representations
This work addresses a bottleneck for researchers and practitioners in audio and signal processing by extending NMF to more flexible signal classes, though it appears incremental as it builds on existing NMF concepts.
The paper tackled the limitation of Non-Negative Matrix Factorization (NMF) to regularly-sampled data by reformulating it with learnable functions, enabling its application to irregularly-spaced time-frequency representations like Constant-Q transforms and wavelets.
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 learnable functions (instead of vectors) and show that NMF can be extended to a wider variety of signal classes that need not be regularly sampled.