Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation

Table 1

Summary of the tensors used, their dimensions, and function, in the various shift-invariant factorisation models included in this paper. Tensors that occur in multiple models are not repeated.

SNTF	𝒳	𝑟×𝑛×𝑚	Signal spectrograms
	𝒳	𝑟×𝑛×𝑚	Approximation of 𝒳
	𝒢	𝑟×𝐾	Instrument gains
	𝒯	𝑛×𝑧×𝑛	Translation tensor (freq.)
	𝒜	𝑛×𝐾×𝑝	Instrument basis functions
	𝒮	𝑧×𝐾×𝑚	Note activations
	𝒫	𝑚×𝑝×𝑚	Translation tensor (time)
SSNTF	ℋ	𝑛×𝑧×ℎ	Harmonic dictionary
	𝒲	ℎ×𝐾×𝑝	Harmonic weights
SF-SSNTF	ℱ	𝑛×𝐾×𝑛	Formant filters
SF-SSNTF + N	ℳ	𝑟×𝐿	Noise instrument gains
	ℬ	𝑛×𝐿×𝑞	Noise basis functions
	𝒞	𝐿×𝑚	Noise activations
	𝒬	𝑚×𝑞×𝑚	Noise translation tensor