  We present Vibrato Nonnegative Tensor Factorization, an algorithm for
single-channel unsupervised audio source separation with an application to
separating instrumental or vocal sources with nonstationary pitch from music
recordings. Our approach extends Nonnegative Matrix Factorization for audio
modeling by including local estimates of frequency modulation as cues in the
separation. This permits the modeling and unsupervised separation of vibrato or
glissando musical sources, which is not possible with the basic matrix
factorization formulation.
  The algorithm factorizes a sparse nonnegative tensor comprising the audio
spectrogram and local frequency-slope-to-frequency ratios, which are estimated
at each time-frequency bin using the Distributed Derivative Method. The use of
local frequency modulations as separation cues is motivated by the principle of
common fate partial grouping from Auditory Scene Analysis, which hypothesizes
that each latent source in a mixture is characterized perceptually by coherent
frequency and amplitude modulations shared by its component partials. We derive
multiplicative factor updates by Minorization-Maximization, which guarantees
convergence to a local optimum by iteration. We then compare our method to the
baseline on two separation tasks: one considers synthetic vibrato notes, while
the other considers vibrato string instrument recordings.
