Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis
We present a system for adaptive spectral basis decomposition that learns to identify independent spectral features given a sequence of short-term Fourier spectra. When applied to recordings of polyphonic piano music, the individual notes are identified as salient features, and hence each short-term spectrum is decomposed into a sum of note spectra; the resulting encoding can be used as a basis for polyphonic transcription. The system is based on a probabilistic model equivalent to a form of noisy independent component analysis (ICA) or sparse coding with non-negativity constraints. We introduce a novel modification to this model that recognises that a short-term Fourier spectrum can be thought of as a noisy realisation of the power spectral density of an underlying Gaussian process, where the noise is essentially multiplicative and non-Gaussian. Results are presented for an analysis of a live recording of polyphonic piano music.