Nonparametric Clustering

The use of density estimation to find clusters in data is supplementing ad hoc hierarchical methodology. Examples include finding high-density regions, finding modes in a kernel density estimator, and the mode tree. Alternatively, a mixture model may be fit and the mixture components associated with individual clusters. Fitting a high-dimensional mixture model with many components is difficult to estimate in practice. Here, we survey mode and level set methods for finding clusters. We describe a new algorithm that estimates a subset of a mixture model. In particular, we demonstrate how to fit one component at a time and how the fits may be organized to reveal the complete clustering model.