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Non-negative matrix factorization (NMF) has been one of the most useful techniques for musical signal analysis in recent years. In particular, supervised NMF, in which a large number of instrumental samples are used for the analysis, is garnering much attention with respect to analytical accuracy and speed. The accuracy, however, deteriorates if the system does not have enough samples. Therefore, in principle, such methods require as many samples as possible in order for the analysis to be accurate. In this paper, we propose an analysis method that 1) does not require the collection of a large number of training samples, and 2) combines the NMF and probabilistic approaches. In this approach, it is assumed that each instrumental category has a model-invariant feature, called a probabilistic spectral envelope (PSE). As an extension of a spectral envelope, this feature represents the probabilities of spectral envelopes belonging to the instrumental category in a two-dimensional (frequency-amplitude) space. The analysis of an input musical signal is carried out using a supervised NMF framework, where the basis matrix contains the optimum spectra that have been generated from pretrained PSEs.

Probabilistic spectral envelope modeling of musical instruments within the non-negative matrix factorization framework for mixed music analysis