A Performance Analysis on Matrix Factorisations in Solving Musical Instrument Source Separation Problem

Abstract

Audio signal decomposition breaks a mixture of musical instrument audio signals into its fundamental musical instrument components. Machine learning is one of the methods widely used in audio signal decomposition. However, the limitation of computer hardware and the complexity of the algorithm may cause the computational speed of machine learning to deteriorate. This paper aims to use the contemporary matrix factorisation to extract the fundamental musical instrument audio signal component from the mixture of musical instrument audio signals. We choose nine contemporary matrix factorisation techniques and compare their performance in separating the mixture of musical instrument audio signals. We create five scenarios with different melody complexity to test the matrix factorisation techniques. Based on the Signal-to-Noise Ratio, Nonnegative Matrix Factorisation with Kullback-Leibler Divergence (NMF-KL) is the best separation performance when the monotonic noise is not added to the mixture of musical instrument audio signals. Initially, NMF-KL has good separation when monotonic noise is added to the simple recurring mixture of musical instrument audio signals, but as the melody complexity increases the NMF-KL separation performance starts to deteriorate. Lastly, the matrix factorisation techniques do not work well when the white noise is added to the mixture of musical instrument audio signals.