2025/07/16 by Alisha L. Foster, Robert J. Webber, Foster, Alisha L. +1
Computer Science · #Audio and Speech Processing (eess.AS) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Music Technology and Sound Studies #Music and Audio Processing #Numerical Analysis (math.NA) #Sound (cs.SD) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2507.12596
openalex publication_date 2025/07/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
How can we process a piece of recorded music to detect and visualize the onset of each instrument? A simple, interpretable approach is based on partially fixed nonnegative matrix factorization (NMF). Yet despite the method's simplicity, partially fixed NMF is challenging to apply because the associated optimization problem is high-dimensional and non-convex. This paper explores two optimization approaches that preserve the nonnegative structure, including a multiplicative update rule and projected gradient descent with momentum. These techniques are derived from the previous literature, but they have not been fully developed for partially fixed NMF before now. Results indicate that projected gradient descent with momentum leads to the higher accuracy among the two methods, and it satisfies stronger local convergence guarantees.