2019/06/17 by Anthony Degleris, Nicolas Gillis, Degleris, Anthony +1 · 1 citation
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Speech and Audio Processing
paper · pdf · doi:10.48550/arxiv.1906.06899
openalex publication_date 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a provably correct algorithm for convolutive\nnonnegative matrix factorization (CNMF) under separability assumptions. CNMF is\na convolutive variant of nonnegative matrix factorization (NMF), which\nfunctions as an NMF with additional sequential structure. This model is useful\nin a number of applications, such as audio source separation and neural\nsequence identification. While a number of heuristic algorithms have been\nproposed to solve CNMF, to the best of our knowledge no provably correct\nalgorithms have been developed. We present an algorithm that takes advantage of\nthe NMF model underlying CNMF and exploits existing algorithms for separable\nNMF to provably find a solution under certain conditions. Our approach\nguarantees the solution in low noise settings, and runs in polynomial time. We\nillustrate its effectiveness on synthetic datasets, and on a singing bird audio\nsequence.\n