A Hierarchical Latent Mixture Model for Polyphonic Music Analysis

Abstract

Polyphonic music transcription is a challenging problem, requiring the identification of a collection of latent pitches which can explain an observed music signal. Many state-of-the-art methods are based on the Non-negative Matrix Factorization (NMF) framework, which itself can be cast as a latent variable model. However, the basic NMF algorithm fails to consider many important aspects of music signals such as low-rank or hierarchical structure and temporal continuity. In this work we propose a probabilistic model to address some of the shortcomings of NMF. Probabilistic Latent Component Analysis (PLCA) provides a probabilistic interpretation of NMF and has been widely applied to problems in audio signal processing. Based on PLCA, we propose an algorithm which represents signals using a collection of low-rank dictionaries built from a base pitch dictionary. This allows each dictionary to specialize to a given chord or interval template which will be used to represent collections of similar frames. Experiments on a standard music transcription data set show that our method can successfully decompose signals into a hierarchical and smooth structure, improving the quality of the transcription.