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 (NMFKL) 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 NMFKL 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.