Bayesian Non-parametric Parsimonious Gaussian Mixture for Clustering

Clustering is one of the essential tasks in machine learning and statistical pattern recognition. One of the most popular approaches in cluster analysis is the one based on the parametric finite mixture model. However, often, parametric models are not well adapted to represent complex and realistic data sets. Another issue in the finite mixture model-based clustering approach is the one of selecting the number of mixture components. The Bayesian non-parametric statistical methods for clustering provide a principled way to overcome these issues. This paper proposes a new Bayesian non-parametric approach for clustering. It relies on an Infinite Gaussian mixture model with an Eigen value decomposition of the covariance matrix of each cluster, and a Chinese Restaurant Process (CRP) prior over the hidden partition. The CRP prior allows to control the model complexity in a principled way, and to automatically learn the number of clusters from the data. The covariance matrix decomposition allows to fit various flexible models going from simplest spherical ones to the more complex general one. We develop a Gibbs sampler to learn the various models and apply it to simulated data and benchmarks, and a real-world data issued from a challenging problem of whale song decomposition. The obtained results highlight the interest of the proposed non-parametric parsimonious mixture model for clustering.