Music Analysis Using Hidden Markov Mixture Models

• Published in: IEEE transactions on signal processing 2007-11, Vol.55 (11), p.5209-5224
• Main Authors: Yuting Qi, Paisley, J.W., Carin, L.
• Format: Article
• Language: English
• Subjects: Applied sciences; Bayesian analysis; Bayesian methods; Computation; Dirichlet problem; Dirichlet process; Exact sciences and technology; Gaussian; hidden Markov model (HMM) mixture; Hidden Markov models; Information, signal and communications theory; Libraries; Machine learning; Markov analysis; Markov chain Monte Carlo (MCMC); Markov processes; Mathematical models; Monte Carlo methods; Multiple signal classification; Music; Music information retrieval; Robustness; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Similarity; Statistical distributions; Studies; Telecommunications and information theory; variational Bayes
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.898782

We develop a hidden Markov mixture model based on a Dirichlet process (DP) prior, for representation of the statistics of sequential data for which a single hidden Markov model (HMM) may not be sufficient. The DP prior has an intrinsic clustering property that encourages parameter sharing, and this naturally reveals the proper number of mixture components. The evaluation of posterior distributions for all model parameters is achieved in two ways: 1) via a rigorous Markov chain Monte Carlo method; and 2) approximately and efficiently via a variational Bayes formulation. Using DP HMM mixture models in a Bayesian setting, we propose a novel scheme for music analysis, highlighting the effectiveness of the DP HMM mixture model. Music is treated as a time-series data sequence and each music piece is represented as a mixture of HMMs. We approximate the similarity of two music pieces by computing the distance between the associated HMM mixtures. Experimental results are presented for synthesized sequential data and from classical music clips. Music similarities computed using DP HMM mixture modeling are compared to those computed from Gaussian mixture modeling, for which the mixture modeling is also performed using DP. The results show that the performance of DP HMM mixture modeling exceeds that of the DP Gaussian mixture modeling.