Transcribing Bach Chorales Limitations and Potentials of Non-Negative Matrix Factorisation

This article discusses our research on polyphonic music transcription using non-negative matrix factorisation (NMF). The application of NMF in polyphonic transcription offers an alternative approach in which observed frequency spectra from polyphonic audio could be seen as an aggregation of spectra from monophonic components. However, it is not easy to find accurate aggregations using a standard NMF procedure since there are many ways to satisfy the factoring of V ≈ WH. Three limitations associated with the application of standard NMF to factor frequency spectra are (i) the permutation of transcription output; (ii) the unknown factoring r; and (iii) the factoring W and H that have a tendency to be trapped in a sub-optimal solution. This work explores the uses of the heuristics that exploit the harmonic information of each pitch to tackle these limitations. In our implementation, this harmonic information is learned from the training data consisting of the pitches from a desired instrument, while the unknown effective r is approximated from the correlation between the input signal and the training data. This approach offers an effective exploitation of the domain knowledge. The empirical results show that the proposed approach could significantly improve the accuracy of the transcription output as compared to the standard NMF approach.