Supervised nonnegative matrix factorization using active-period-aware structured ℓ1-norm for music transcription

An active-period-aware supervised nonnegative matrix factorization (NMF) approach for music transcription is proposed. Supervised NMF relies on a set of known spectrograms associated with all musical instruments that may possibly be involved with given music data; this is supported by the availability of large database of a variety of musical instruments. It is free from the source-number determination problem and this is a significant advantage over the unsupervised NMF approaches. The proposed approach is composed of three steps. Step 1: Apply the existing supervised NMF algorithm. Step 2: Estimate the ‘active’ periods (during which musical sounds are present) based on the outcomes of Step 1. Step 3: Optimize a refined cost function reflecting the estimate of active periods. The awareness of active periods leads to avoidance of the so-called octave-errors which is a central issue of the existing supervised NMF method. Simulation results show the efficacy of the proposed approach.1