Nonnegative Matrix Factorization with Transform Learning
This is an incremental improvement for audio signal processing, as it adapts NMF by learning transforms rather than using pre-fixed ones.
The paper tackles the problem of signal decomposition by relaxing the fixed transform in traditional nonnegative matrix factorization (NMF) and jointly learning a short-time orthogonal transform with the factorization, resulting in a novel algorithm tested on audio signal processing experiments.
Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn a short-time orthogonal transform together with the factorization. To this end, we formulate a regularized optimization problem reminiscent of conventional NMF, yet with the transform as additional unknown parameters, and design a novel block-descent algorithm enabling to find stationary points of this objective function. The proposed joint transform learning and factorization approach is tested for two audio signal processing experiments, illustrating its conceptual and practical benefits.